 
Summary: Partial Least Squares (PLS) Regression.
Herv´e Abdi1
The University of Texas at Dallas
Introduction
Pls regression is a recent technique that generalizes and combines features
from principal component analysis and multiple regression. It is particularly
useful when we need to predict a set of dependent variables from a (very) large
set of independent variables (i.e., predictors). It originated in the social sciences
(specifically economy, Herman Wold 1966) but became popular first in chemo
metrics (i.e., computational chemistry) due in part to Herman's son Svante,
(see, e.g., Geladi & Kowalski, 1986) and in sensory evaluation (Martens & Naes,
1989). But pls regression is also becoming a tool of choice in the social sciences
as a multivariate technique for nonexperimental and experimental data alike
(e.g., neuroimaging, see Mcintosh, Bookstein, Haxby, & Grady, 1996). It was
first presented as an algorithm akin to the power method (used for computing
eigenvectors) but was rapidly interpreted in a statistical framework. (Frank, &
Friedman, 1993; Helland, 1990; H¨oskuldsson, 1988; Tenenhaus, 1998).
Prerequisite notions and notations
The I observations described by K dependent variables are stored in a I ×K
matrix denoted Y, the values of J predictors collected on these I observations
