Indefinite kernel discriminant analysis

Abstract

Kernel methods for data analysis are frequently considered to be restricted to positive definite kernels. In practice, however, indefinite kernels arise e.g. from problem-specific kernel construction or optimized similarity measures. We, therefore, present formal extensions of some kernel discriminant analysis methods which can be used with indefinite kernels. In particular these are the multi-class kernel Fisher discriminant and the kernel Mahalanobis distance. The approaches are empirically evaluated in classification scenarios on indefinite multi-class datasets. © Springer-Verlag Berlin Heidelberg 2010.