Gradient-Based Optimization of Kernel Polarization for RBF Kernels

The problem of model selection for support vector machines using the RBF kernels is considered. We introduce a geometric view on maximizing kernel polarization, which intuitively shows why we choose kernel polarization as the criterion for kernel selection. After that we propose a gradient-based method for learning the width parameter of RBF kernels. This method is based on the possibility of computing the gradient of kernel polarization with respect to the width parameter. The proposed method is demonstrated with some UCI machine learning benchmark examples.