文档介绍：Partial Least Square Regression
PLS-Regression
Hervé Abdi1
1 Overview
PLS regression is a recent technique that generalizes bines
features from ponent analysis and multiple regres-
sion. Its goal is to predict or analyze a set of dependent variables
from a set of independent variables or predictors. This predic-
tion is achieved by extracting from the predictors a set of orthog-
onal factors called latent variables which have the best predictive
power.
PLS regression is particularly useful when we need to predict
a set of dependent variables from a (very) large set of indepen-
dent variables (., predictors). It originated in the social sciences
(specifically economy, Herman Wold 1966) but became popular
first in chemometrics (., computational chemistry) due in part
to Herman’s son Svante, (Wold, 2001) and in sensory evaluation
(Martens & Naes, 1989). But PLS regression is also ing a tool
of choice in the social sciences as a multivariate technique for non-
experimental and experimental data alike (., neuroimaging, see
Mcintosh & Lobaugh, 2004; Worsley, 1997). It was first presented
1In: Neil Salkind (Ed.) (2007). Encyclopedia of Measurement and Statistics.
Thousand Oaks (CA): Sage.
Address correspondence to: Hervé Abdi
Program in Cognition and Neurosciences, MS: ,
The University of Texas at Dallas,
Richardson, TX 75083–0688, USA
E-mail: ******@ /∼herve
1
Hervé Abdi: PLS-Regression
as an algorithm akin to the power method (used puting
eigenvectors) but was rapidly interpreted in a statistical framework.
(see ., Phatak, & de Jong, 1997; Tenenhaus, 1998; Ter Braak & de
Jong, 1998).
2 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 are collected in the I × J matrix X.
3 Goal of PLS regression:
Predict Y from X
The goal of PLS regression is to predict Y from X a