Implementing a new method for discriminant analysis when group covariance matrices are nearly singular

We consider a uni ed description of classi cation rules for nearly singular covariance matrices. When the covariance matrices of the groups or the pooled covariance matrix become nearly singular, bayesian classi cation rules become seriously unstable. Several procedures have been proposed to tackle this problem, e.g. SIMCA, and Regularized Discriminant Analysis. N s and Indahl (1998) discovered common properties for all of these procedures and proposed a uni ed classi er that incorporates the functionality of them all. Since the uni ed approach needs many parameters, they also proposed an alternative classi er with fewer parameters. We implemented both classi ers and compared them in a simulation study to the procedures RDA, LDA, and QDA. To enhance the comparability of our results we based the simulation study on the study of Friedman (1989). In the implementation, we used a combination of the Nelder-Mead Simplexalgorithm and Simulated Annealing (Bohachevsky et al. (1986)) to optimize the classi cation error directly.