Comparative Performance of Several Robust Linear Discriminant Analysis Methods

Abstract

The problem of the non-robustness of the classical estimates in the setting of the quadratic and linear discriminant analysis has been addressed by many authors: Todorov et al. [19, 20], Chork and Rousseeuw [1], Hawkins and McLachlan [4], He and Fung [5], Croux and Dehon [2], Hubert and Van Driessen [6]. To obtain high breakdown these methods are based on high breakdown point estimators of location and covariance matrix like MVE, MCD and S. Most of the authors use also one step re-weighting after the high breakdown point estimation in order to obtain increased efficiency. We propose to use M-iteration as described by Woodruff and Rocke [22] instead, since this is the preferred means of achieving efficiency with high breakdown. Further we experiment with the pairwise class of algorithms proposed by Maronna and Zamar [10] which were not used up to now in the context of discriminant analysis. The available methods for robust linear discriminant analysis are compared on two real data sets and on a large scale simulation study. These methods are implemented as R functions in the package for robust multivariate analysis rrcov.