Analytical study of performance of linear discriminant analysis in stochastic settings

PATTERN RECOGNITION

卷:46

Article

Zollanvari, Amin^1,2  Hua, Jianping³  Dougherty, Edward R.^1,3 

[1] Texas A&M Univ, Dept Elect & Comp Engn, College Stn, TX 77843 USA

[2] Texas A&M Univ, Dept Stat, College Stn, TX 77843 USA

[3] Translat Genom Res Inst TGEN, Phoenix, AZ 85004 USA

关键词: Linear discriminant analysis;    Stochastic settings;    Correlated data;    Non-i.i.d data;    Expected error;    Gaussian processes;    Auto-regressive models;    Moving-average models;   

DOI  :  10.1016/j.patcog.2013.04.002

来源: Elsevier

【 摘 要 】

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. Published by Elsevier Ltd.

【 授权许可】

Free