Discriminant analysis under the common principal components model

Pepler, P.T. , Uys, D.W. and Nel, D.G. (2017) Discriminant analysis under the common principal components model. Communications in Statistics: Simulation and Computation, 46(6), pp. 4812-4827. (doi: 10.1080/03610918.2015.1134568)

Abstract

For two or more populations of which the covariance matrices have a common set of eigenvectors, but different sets of eigenvalues, the common principal components (CPC) model is appropriate. Pepler et al. (2015) proposed a regularised CPC covariance matrix estimator and showed that this estimator outperforms the unbiased and pooled estimators in situations where the CPC model is applicable. This paper extends their work to the context of discriminant analysis for two groups, by plugging the regularised CPC estimator into the ordinary quadratic discriminant function. Monte Carlo simulation results show that CPC discriminant analysis offers significant improvements in misclassification error rates in certain situations, and at worst performs similar to ordinary quadratic and linear discriminant analysis. Based on these results, CPC discriminant analysis is recommended for situations where the sample size is small compared to the number of variables, in particular for cases where there is uncertainty about the population covariance matrix structures.

• Item Type: Articles
• Keywords: Common principal components, Discriminant analysis, Covariance matrix, Monte Carlo simulation
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Pepler, Dr Theo
• Authors: Pepler, P.T., Uys, D.W., and Nel, D.G.
• College/School: College of Medical Veterinary and Life Sciences > School of Biodiversity, One Health & Veterinary Medicine
• Journal Name: Communications in Statistics: Simulation and Computation
• Publisher: Taylor & Francis
• ISSN: 0361-0918
• ISSN (Online): 1532-4141
• Published Online: 13 January 2016
• Copyright Holders: Copyright © 2016 Taylor and Francis
• First Published: First published in Communications in Statistics - Simulation and Computation 46(6):4812-4827
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher