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An alternative nonlinear multiclass discriminant algorithm is presented. This algorithm is based on the use of kernel functions and is designed to optimize a general linear discriminant analysis criterion based on scatter matrices. By reformulating these matrices in a specific form, a straightforward derivation allows the kernel function to be introduced in a simple and direct way. Moreover, we propose a method to determine the value of the regularization parameter , based on this derivation.doi:10.1109/lsp.2003.813680 fatcat:4kx7go2ysfdkroti2nhylcf2au