Constructing descriptive and discriminative nonlinear features: Rayleigh coefficients in kernel feature spaces

We incorporate prior knowledge to construct nonlinear algorithms for invariant feature extraction and discrimination. Employing a unified framework in terms of a nonlinearized variant of the Rayleigh coefficient, we propose nonlinear generalizations of Fisher´s discriminant and oriented PCA using support vector kernel functions. Extensive simulations show the utility of our approach.