Regularized discriminant analysis with optimally scaled data

Linear discriminant analysis is a well known procedure of discrimination which is equivalent to canonical correlation analysis where the Linear predictors define one set of variables, and a set of dummy variables representing class membership defines the other set. Here we propose a new way of discrimination of observations explained by a set of variables with mixed scaling level. We use a nonparametric discriminant procedure based an optimally scaling the data to estimate the distribution of the object scores. Next, we propose a multivariate kernel distribution of the variables with a variety of window widths which controls the degree of smoothness of the estimate. We choose the window width of the kernel distribution and the dimension of object scores matrix by cross-validation (leave-one-out).