An Adaptive Gaussian Kernel for Support Vector Machine

The most commonly used kernel function of support vector machine (SVM) in nonlinear separable dataset in machine learning is Gaussian kernel, also known as radial basis function. The Gaussian kernel decays exponentially in the input feature space and uniformly in all directions around the support vector, causing hyper-spherical contours of kernel function. In this study, an adaptive kernel function is designed based on the Gaussian kernel, which is used in SVM. While the sigma parameter is determined as an arbitrary value in the traditional Gaussian kernel, a modified Gaussian kernel method is used that calculates an adaptive value depending on the input vectors in the proposed kernel function. The proposed kernel function is compared with the linear, polynomial and Gaussian kernels commonly used in support vector machines. The results show that the proposed kernel function performs well on separable linear and nonlinear datasets compared to other kernel functions. It is also compared to state-of-the-art support vector machine kernels.