 
Summary: Partial Least Squares Methods:
Partial Least Squares Correlation and Partial Least Square Regression
Herv´e Abdi *
School of Behavioral and Brain Sciences
The University of Texas at Dallas
Lynne J. Williams
Rotman Research Institute at Baycrest (Toronto CA)
* Corresponding author: Herv´e Abdi, School of Behavioral and Brain Sciences, The University of Texas at Dallas,
MS: GR4.1, 800 West Campbell Road, Richardson, TX 750803021, USA Email: herve@utdallas.edu
to appear in:
B. Reisfeld and A. Mayeno (Eds.), Methods in Molecular Biology:Computational Toxicology. New York: Springer
Verlag.
Abstract
Partial least square (PLS) methods (also sometimes called projection to latent structures) relate the information
present in two data tables that collect measurements on the same set of observations. PLS methods proceed by deriving
latent variables which are (optimal) linear combinations of the variables of a data table. When the goal is to find the
shared information between two tables, the approach is equivalent to a correlation problem and the technique is then
called partial least square correlation (PLSC) (also sometimes called PLSSVD). In this case there are two sets of
latent variables (one set per table), and these latent variables are required to have maximal covariance. When the
goal is to predict one data table the other one, the technique is then called partial least square regression In this case
