Regularized kernel discriminant analysis with optimally scaled data

Linear discriminant analysis is a well known procedure for discrimination where the linear predictors define one set of variables and a set of dummy variables representing class membership which defines the other set. Here we propose a new method of discriminating between observations using a set of mixed (i.e., categorical and/or continuous) variables. This nonparametric discriminant procedure optimally scales the data and estimates the distribution of the object scores using multivariate kernel density estimation. We propose using Bozdogan's information-theoretic measure complexity ICOMP to select both the window width of the kernel density estimator as well as the dimension of the object scores matrix.