A method for designing nonlinear Kernel-based discriminant functions from the class of second-order criteria

A simple method to derive a nonlinear discriminant is to map samples into a high dimensional space F using a nonlinear function and then to perform a linear discriminant analysis. Using Mercer kernels, this problem can be solved without explicitly mapping into F. Recently, a powerful method of obtaining the nonlinear kernel Fisher discriminant based on Mercer kernels was proposed. Here, we present an extension of this method that consists in determining the optimum nonlinear receiver in the sense of the best second-order criterion, without setting it up. Mercer functions allow obtaining a closed form solution to this problem.