Joint Selection of Central and Extremal Prototypes Based on Kernel Minimum Enclosing Balls

We present a simple, two step procedure that selects central and extremal prototypes from a given set of data. The key idea is to identify minima of the function that characterizes the interior of a kernel minimum enclosing ball of the data. We discuss how to efficiently compute kernel minimim enclosing balls using the Frank-Wolfe algorithm and show that, for Gaussian kernels, the sought after prototypes can be naturally found via a variant of the mean shift procedure. Practical results demonstrate that prototypes found this way are descriptive, meaningful, and interpretable.