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Bioinformatics Advance Access originally published online on October 25, 2005
Bioinformatics 2006 22(1):88-95; doi:10.1093/bioinformatics/bti736
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© The Author 2005. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Gene selection using support vector machines with non-convex penalty

Hao Helen Zhang 1,*, Jeongyoun Ahn 2, Xiaodong Lin 3 and Cheolwoo Park 4

1Department of Statistics, North Carolina State University Raleigh, NC 27695, USA
2Department of Statistics and Operations Research, University of North Carolina Chapel Hill, NC 27599, USA
3Department of Mathematical Sciences, University of Cincinnati OH 45221, USA
4Department of Statistics, University of Georgia Athens, GA 30602, USA

*To whom correspondence should be addressed.

Motivation: With the development of DNA microarray technology, scientists can now measure the expression levels of thousands of genes simultaneously in one single experiment. One current difficulty in interpreting microarray data comes from their innate nature of ‘high-dimensional low sample size’. Therefore, robust and accurate gene selection methods are required to identify differentially expressed group of genes across different samples, e.g. between cancerous and normal cells. Successful gene selection will help to classify different cancer types, lead to a better understanding of genetic signatures in cancers and improve treatment strategies. Although gene selection and cancer classification are two closely related problems, most existing approaches handle them separately by selecting genes prior to classification. We provide a unified procedure for simultaneous gene selection and cancer classification, achieving high accuracy in both aspects.

Results: In this paper we develop a novel type of regularization in support vector machines (SVMs) to identify important genes for cancer classification. A special nonconvex penalty, called the smoothly clipped absolute deviation penalty, is imposed on the hinge loss function in the SVM. By systematically thresholding small estimates to zeros, the new procedure eliminates redundant genes automatically and yields a compact and accurate classifier. A successive quadratic algorithm is proposed to convert the non-differentiable and non-convex optimization problem into easily solved linear equation systems. The method is applied to two real datasets and has produced very promising results.

Availability: MATLAB codes are available upon request from the authors.

Contact: hzhang{at}stat.ncsu.edu

Supplementary information: http://www4.stat.ncsu.edu/~hzhang/research.html

Received on June 12, 2005; revised on October 20, 2005; accepted on October 20, 2005

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