On partial least squares dimension reduction for microarray-based classification: a simulation study

In microarray tumor tissue classi'cation studies, the expressions of thousands of genes (variables) are simultaneously measured across a few tissue samples. Standard statistical methodologies in classi'cation do not work well when the dimension, p, is greater than the sample size, N . One approach to classi'cation problems, when p N , is to 'rst apply a dimension reduction method and then perform the classi'cation in the reduced space. In this paper, we study dimension reduction for classi'cation in high dimension based on partial least squares (PLS) and principal components analysis (PCA). In addition, we propose and explore two hybrid-PLS methods for dimension reduction. PLS components are linear combinations of the original predictors, but the weights are nonlinear functions of both the predictors and response variable. This makes it di:cult to study the PLS classi'cation methodologies analytically, so, in this paper, we turn to a numerical study using simulation. c © 2003 Elsevier B.V. All rights reserved.