Analytical study of performance of linear discriminant analysis in stochastic settings

Amin Zollanvari, Jianping Hua, Edward R. Dougherty

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)3017-3029
Number of pages13
JournalPattern Recognition
Issue number11
Publication statusPublished - Nov 2013
Externally publishedYes


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

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Artificial Intelligence

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