A Novel Hybrid Dimension Reduction Technique for Undersized High Dimensional Gene Expression Data Sets Using Information Complexity Criterion for Cancer Classification
Open Access
- 1 January 2015
- journal article
- research article
- Published by Hindawi Limited in Computational and Mathematical Methods in Medicine
- Vol. 2015, 1-14
- https://doi.org/10.1155/2015/370640
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.Keywords
Funding Information
- Council of Higher Education of Turkey
This publication has 26 references indexed in Scilit:
- Probabilistic principal component analysis for metabolomic dataBMC Bioinformatics, 2010
- Identification of differential gene pathways with principal component analysisBioinformatics, 2009
- Principal component analysis of native ensembles of biomolecular structures (PCA_NEST): insights into functional dynamicsBioinformatics, 2009
- Supervised principal component analysis for gene set enrichment of microarray data with continuous or survival outcomesBioinformatics, 2008
- Independent component analysis-based penalized discriminant method for tumor classification using gene expression dataBioinformatics, 2006
- Prediction of central nervous system embryonal tumour outcome based on gene expressionNature, 2002
- Akaike's Information Criterion and Recent Developments in Information ComplexityJournal of Mathematical Psychology, 2000
- Distinct types of diffuse large B-cell lymphoma identified by gene expression profilingNature, 2000
- On the information-based measure of covariance complexity and its application to the evaluation of multivariate linear modelsCommunications in Statistics - Theory and Methods, 1990
- Empirical Bayes Estimation of the Multivariate Normal Covariance MatrixThe Annals of Statistics, 1980