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GD-RDA: A New Regularized Discriminant Analysis for High-Dimensional Data.

Authors
  • Zhou, Yan1
  • Zhang, Baoxue2
  • Li, Gaorong3
  • Tong, Tiejun4
  • Wan, Xiang5
  • 1 1 College of Mathematics and Statistics, Institute of Statistical Sciences, Shenzhen University , ShenZhen, China . , (China)
  • 2 2 School of Statistics, Capital University of Economics and Business , Beijing, China . , (China)
  • 3 3 Beijing Institute for Scientific and Engineering Computing, Beijing University of Technology , Beijing, China . , (China)
  • 4 4 Department of Mathematics, Hong Kong Baptist University , Hong Kong, China . , (China)
  • 5 5 Department of Computer Science, Hong Kong Baptist University , Hong Kong, China . , (China)
Type
Published Article
Journal
Journal of Computational Biology
Publisher
Mary Ann Liebert
Publication Date
Nov 01, 2017
Volume
24
Issue
11
Pages
1099–1111
Identifiers
DOI: 10.1089/cmb.2017.0029
PMID: 28414553
Source
Medline
Keywords
License
Unknown

Abstract

High-throughput techniques bring novel tools and also statistical challenges to genomic research. Identification of which type of diseases a new patient belongs to has been recognized as an important problem. For high-dimensional small sample size data, the classical discriminant methods suffer from the singularity problem and are, therefore, no longer applicable in practice. In this article, we propose a geometric diagonalization method for the regularized discriminant analysis. We then consider a bias correction to further improve the proposed method. Simulation studies show that the proposed method performs better than, or at least as well as, the existing methods in a wide range of settings. A microarray dataset and an RNA-seq dataset are also analyzed and they demonstrate the superiority of the proposed method over the existing competitors, especially when the number of samples is small or the number of genes is large. Finally, we have developed an R package called "GDRDA" which is available upon request.

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