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Computational and Mathematical Methods in Medicine
Volume 2015 (2015), Article ID 370640, 14 pages
http://dx.doi.org/10.1155/2015/370640
Research Article

A Novel Hybrid Dimension Reduction Technique for Undersized High Dimensional Gene Expression Data Sets Using Information Complexity Criterion for Cancer Classification

1Department of Statistics, Faculty of Science, Firat University, 23119 Elazig, Turkey
2Department of Business Analytics and Statistics, The University of Tennessee, Knoxville, TN 37996, USA

Received 24 December 2014; Accepted 18 February 2015

Academic Editor: David A. Winkler

Copyright © 2015 Esra Pamukçu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Gene expression data typically are large, complex, and highly noisy. Their dimension is high with several thousand genes (i.e., features) but with only a limited number of observations (i.e., samples). Although the classical principal component analysis (PCA) method is widely used as a first standard step in dimension reduction and in supervised and unsupervised classification, it suffers from several shortcomings in the case of data sets involving undersized samples, since the sample covariance matrix degenerates and becomes singular. In this paper we address these limitations within the context of probabilistic PCA (PPCA) by introducing and developing a new and novel approach using maximum entropy covariance matrix and its hybridized smoothed covariance estimators. To reduce the dimensionality of the data and to choose the number of probabilistic PCs (PPCs) to be retained, we further introduce and develop celebrated Akaike’s information criterion (AIC), consistent Akaike’s information criterion (CAIC), and the information theoretic measure of complexity (ICOMP) criterion of Bozdogan. Six publicly available undersized benchmark data sets were analyzed to show the utility, flexibility, and versatility of our approach with hybridized smoothed covariance matrix estimators, which do not degenerate to perform the PPCA to reduce the dimension and to carry out supervised classification of cancer groups in high dimensions.