Gene Expression Data Classification with Revised Kernel Partial Least Squares Algorithm

One important feature of the gene expression data is that the number of genes M far exceeds the number of samples N. Standard statistical methods do not work well when N < M . Development of new methodologies or modification of existing methodologies is needed for the analysis of the microarray data. In this paper, we propose a novel analysis procedure for classifying the gene expression data. This procedure involves dimension reduction using kernel partial least squares (KPLS) and classification with logistic regression (discrimination) and other standard machine learning methods. KPLS is a generalization and nonlinear version of partial least squares (PLS). The proposed algorithm was applied to five different gene expression datasets involving human tumor samples. Comparison with other popular classification methods such as support vector machines and neural networks shows that our algorithm is very promising in classifying gene expression data. Introduction One important application of gene expression data is classification of samples into different categories, such as the types of tumor. Gene expression data are characterized by many variables on only a few observations. It has been observed that although there are thousands of genes for each observation, a few underlying gene components may account for much of the data variation. PLS provides an efficient way to find these underlying gene components and reduce the input dimensions (Nguyen and Rocke 2002). PLS is a method for modeling a linear relationship between a set of output variables and a set of input variables and has been extensively used in chemometrics. In general, the structure of chemometric data is similar to that of microarray data: small samples and high dimensionality. With this type of inputs, linear least squares regression often fails, but linear PLS excels. Rosipal and Trejo (2001) and Bennett and Embrechts (2003) extended PLS to nonlinear regression using kernel functions, mainly for the purpose of real value predictions. Nguyen and Rocke (2002) applied PLS/PCA, together with logistic discrimination, to classify the tumor data and Copyright c © 2004, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. claimed success of their approach. However, their procedure is linear and limited with the implementation of SAS. In this paper we propose a novel analysis procedure for classification of tumor samples using gene expression profiles. Our algorithm combines KPLS with logistic regression. Involved in our procedure are three steps: feature space transformation, dimension reduction, and classification. The proposed algorithm has been applied to five different popular gene expression datasets. One is a two-class recognition problem (AML versus ALL), and the other four concern multiple classes. Algorithm A gene expression dataset with M genes (features) and N mRNA samples (observations) can be conveniently represented by the following gene expression matrix