Random radial basis function kernel-based support vector machine

Abstract The main computational cost of building a support vector machine (SVM) training model lies in tuning the hyperparameters, including the kernel parameters and penalty constant C . This paper introduces a new kernel, the random radial basis function (RRBF) kernel, which all kernel parameters can be assigned to randomly. The key idea of the RRBF is to extend a one-dimensional parameter to d -dimensional parameters by simple modification of the traditional RBF kernel. We prove the universal approximation capability of a SVM with the RRBF kernel, proposing a simple model selection algorithm. The experiments on benchmark datasets show that SVM with the RRBF kernel clearly outperforms the traditional RBF kernel and other popular kernels, and the results are quite insensitive to C . Compared with other kernels, a SVM with the RRBF kernel is not sensitive to the penalty constant C , and it can be tuned in a wide range. Additionally, this property also enables a SVM to find the hyperparameters quickly. A simulation of parameter sensitivity study also show that a SVM is more stable w.r.t. to the different choices of kernel parameters.