High Breakdown Linear Discriminant Analysis

The classiication rules of linear discriminant analysis are deened by the true mean vectors and the common covariance matrix of the populations from which the data come. As these true parameters are in general unknown, they are commonly estimated by the sample mean vector and covariance matrix of the data in a training sample randomly drawn from each population. These sample statistics are however notoriously susceptible to contamination by outliers, a problem compounded by the fact that the outliers may be invisible to conventional diagnostics. High breakdown estimation is a procedure designed to remove this cause for concern by producing estimates that are immune to serious distortion by a minority of outliers, regardless of their severity. In this paper, we motivate and develop a high breakdown criterion for linear discriminant analysis and give an algorithm for