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Bioinformatics Advance Access published online on November 30, 2004
Bioinformatics, doi:10.1093/bioinformatics/bti171
Bioinformatics © Oxford University Press 2004; all rights reserved
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Received September 16, 2004
Revised November 17, 2004
Accepted November 19, 2004

Article

Optimal number of features as a function of sample size for various classification rules

Jianping Hua 1, Zixiang Xiong 1, James Lowey 2, Edward Suh 2, and Edward R. Dougherty 3*

1 Dept of Electrical Engineering, Texas A&M University, College Station, TX 77843, USA
2 Translational Genomics Research Institute, Phoenix, AZ 85004, USA
3 Dept of Electrical Engineering, Texas A&M University, College Station, TX 77843, USA; Department of Pathology, University of Texas M.D. Anderson Cancer Center, Houston, TX 77030, USA

* To whom correspondence should be addressed.
Edward R. Dougherty, E-mail: e-dougherty{at}ee.tamu.edu


  Abstract

Motivation: Given the joint feature-label distribution, increasing the number of features always results in decreased classification error; however, this is not the case when a classifier is designed via a classification rule from sample data. Typically (but not always), for fixed sample size, the error of a designed classifier decreases and then increases as the number of features grows. The potential downside of using too many features is most critical for small samples, which are commonplace for gene-expression-based classifiers for phenotype discrimination. For fixed sample size and feature-label distribution, the issue is to find an optimal number of features.

Results: Since only in rare cases is there a known distribution of the error as a function of the number of features and sample size, this study employs simulation for various feature-label distributions and classification rules, and across a wide range of sample and feature-set sizes. To achieve the desired end, finding the optimal number of features as a function of sample size, it employs massively parallel computation. Seven classifiers are treated: 3-nearest-neighbor, Gaussian kernel, linear support vector machine, polynomial support vector machine, perceptron, regular histogram and linear discriminant analysis. Three Gaussian-based models are considered: linear, nonlinear and bimodal. In addition, real patient data from a large breast-cancer study is considered. To mitigate the combinatorial search for finding optimal feature sets, and to model the situation in which subsets of genes are co-regulated and correlation is internal to these subsets, we assume that the covariance matrix of the features is blocked, with each block corresponding to a group of correlated features. Altogether there is a large number of error surfaces for the many cases. These are provided in full on a companion web-site, which is meant to serve as resource for those working with small-sample classification.

Availability: For the companion web-site, please visit http://public.tgen.org/tamu/ofs/.


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