A Kernel Optimization Method Based on the Localized Kernel Fisher Criterion

Abstract

It is wildly recognized that whether the selected kernel matches the data controls the performance of kernel-based methods. Ideally it is expected that the data is linearly separable in the kernel induced feature space, therefore, Fisher linear discriminant criterion can be used as a kernel optimization rule. However, the data may not be linearly separable even after kernel transformation in many applications, a nonlinear classifier is preferred in this case, and obviously the Fisher criterion is not the best choice as a kernel optimization rule. Motivated by this issue, in this paper we present a novel kernel optimization method by maximizing the local class linear separability in kernel space to increase the local margins between embedded classes via localized kernel Fisher criterion, by which the classification performance of nonlinear classifier in the kernel induced feature space can be improved. Extensive experiments are carried out to evaluate the efficiency of the proposed method.