title: Analytical Study of Performance of Linear Discriminant Analysis in Stochastic Settings.
abstract: This paper provides exact analytical expressions for the first and second moments of the true error for linear discriminant analysis (LDA) when the data are univariate and taken from two stochastic Gaussian processes. The key point is that we assume a general setting in which the sample data from each class do not need to be identically distributed or independent within or between classes. We compare the true errors of designed classifiers under the typical i.i.d. model and when the data are correlated, providing exact expressions and demonstrating that, depending on the covariance structure, correlated data can result in classifiers with either greater error or less error than when training with uncorrelated data. The general theory is applied to autoregressive and moving-average models of the first order, and it is demonstrated using real genomic data.
authors.affiliation: Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX 77843 ; Department of Statistics, Texas A&M University, College Station, TX 77843.
authors.forename: Amin
authors.initials: A
authors.lastname: Zollanvari
authors.forename: Jianping
authors.initials: J
authors.lastname: Hua
authors.forename: Edward R
authors.initials: ER
authors.lastname: Dougherty
keywords: Auto-regressive models; Correlated data; Expected error; Gaussian processes; Linear discriminant analysis; Moving-average models; Non-i.i.d data; Stochastic settings
references.citation: J Clin Oncol. 2002 Mar 15;20(6):1480-90
references.pmid: 11896095
references.citation: Mol Genet Metab. 2006 Dec;89(4):310-5
references.pmid: 17008115
references.citation: Cancer Res. 1992 Dec 1;52(23):6696-8
references.pmid: 1423316
references.citation: Ann Surg. 1992 Jul;216(1):55-9
references.pmid: 1632702
references.citation: Int J Biol Markers. 1998 Oct-Dec;13(4):179-87
references.pmid: 10228898
references.citation: Neoplasia. 2004 Sep-Oct;6(5):541-5
references.pmid: 15548363
references.citation: J Natl Cancer Inst. 2006 Sep 6;98(17):1183-92
references.pmid: 16954471
references.citation: N Engl J Med. 2009 Mar 26;360(13):1320-8
references.pmid: 19297566
references.citation: Nature. 2002 Jan 31;415(6871):530-6
references.pmid: 11823860