Indefinite Kernel Fisher Discriminant

Indefinite kernels arise in practice, e.g. from problem-specific kernel construction. Therefore, it is necessary to understand the behavior and suitability of classifiers in the corresponding indefinite inner product spaces. In this paper we address the Indefinite Kernel Fisher Discriminant (IKFD). First, we give the geometric interpretation of the Fisher Discriminant in indefinite inner product spaces. We show that IKFD is closely related to the well-known formulation of the traditional Kernel Fisher Discriminant derived for positive definite kernels. Practical implications are that IKFD can be directly applied to indefinite kernels without manipulation of the kernel matrix. Experiments demonstrate the geometrically intuitive classification and enable comparisons to other indefinite kernel classifiers.