On the dimension effect of regularized linear discriminant analysis

Cheng Wang, Binyan Jiang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

4 Citations (Scopus)

Abstract

This paper studies the dimension effect of the linear discriminant analysis (LDA) and the regularized linear discriminant analysis (RLDA) classifiers for large dimensional data where the observation dimension p is of the same order as the sample size n. More specifically, built on properties of the Wishart distribution and recent results in random matrix theory, we derive explicit expressions for the asymptotic misclassification errors of LDA and RLDA respectively, from which we gain insights of how dimension affects the performance of classification and in what sense. Motivated by these results, we propose adjusted classifiers by correcting the bias brought by the unequal sample sizes. The bias-corrected LDA and RLDA classifiers are shown to have smaller misclassification rates than LDA and RLDA respectively. Several interesting examples are discussed in detail and the theoretical results on dimension effect are illustrated via extensive simulation studies.

Original languageEnglish
Pages (from-to)2709-2742
Number of pages34
JournalElectronic Journal of Statistics
Volume12
Issue number2
DOIs
Publication statusPublished - Jan 2018

Keywords

  • Dimension effect
  • Linear discriminant analysis
  • Random matrix theory
  • Regularized linear discriminant analysis

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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