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

Fahed Abdallah (1) , Cédric Richard (1) , Régis Lengellé (1)

1 LM2S - Laboratoire Modélisation et Sûreté des Systèmes

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.

Domains: Signal and Image processing

Fahed Abdallah, Cédric Richard, Régis Lengellé. A method for designing nonlinear Kernel-based discriminant functions from the class of second-order criteria. Conference Record of the Thirty-Sixth Asilomar Conference on Signals, Systems and Computers, Nov 2002, Pacific Grove, United States. pp.939-942. ⟨hal-02284330⟩