Linear classifier design under heteroscedasticity in Linear Discriminant Analysis

Kojo Sarfo Gyamfi*, James Brusey, Andrew Hunt, Elena Gaura

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)
28 Downloads (Pure)

Abstract

Under normality and homoscedasticity assumptions, Linear Discriminant Analysis (LDA) is known to be optimal in terms of minimising the Bayes error for binary classification. In the heteroscedastic case, LDA is not guaranteed to minimise this error. Assuming heteroscedasticity, we derive a linear classifier, the Gaussian Linear Discriminant (GLD), that directly minimises the Bayes error for binary classification. In addition, we also propose a local neighbourhood search (LNS) algorithm to obtain a more robust classifier if the data is known to have a non-normal distribution. We evaluate the proposed classifiers on two artificial and ten real-world datasets that cut across a wide range of application areas including handwriting recognition, medical diagnosis and remote sensing, and then compare our algorithm against existing LDA approaches and other linear classifiers. The GLD is shown to outperform the original LDA procedure in terms of the classification accuracy under heteroscedasticity. While it compares favourably with other existing heteroscedastic LDA approaches, the GLD requires as much as 60 times lower training time on some datasets. Our comparison with the support vector machine (SVM) also shows that, the GLD, together with the LNS, requires as much as 150 times lower training time to achieve an equivalent classification accuracy on some of the datasets. Thus, our algorithms can provide a cheap and reliable option for classification in a lot of expert systems.

Original languageEnglish
Pages (from-to)44-52
Number of pages9
JournalExpert Systems With Applications
Volume79
DOIs
Publication statusPublished - 15 Aug 2017
Externally publishedYes

Bibliographical note

Copyright the Author(s) 2017. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

Keywords

  • LDA
  • heteroscedasticity
  • Bayes error
  • linear classifier

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