On local kernel polarization

The problem of evaluating the quality of a kernel function for a classification task is considered. Drawn from physics, kernel polarization was introduced as an effective measure for selecting kernel parameters, which was previously done mostly by exhaustive search. However, it only takes between-class separability into account but neglects the preservation of within-class local structure. The `globality¿ of the kernel polarization may leave less degree of freedom for increasing separability. In this paper, we propose a new quality measure called local kernel polarization, which is a localized variant of kernel polarization. Local kernel polarization can preserve the local structure of the data of the same class so the data can be embedded more appropriately. This quality measure is demonstrated with some UCI machine learning benchmark examples.