Lower C limits in support vector machines with radial basis function kernels

In this paper, a γ dependent lower C limits formula for the effective hyperparameter (C, γ) region for Support Vector Classification (SVC) with Radial Basis Function (RBF) kernel is derived, on the basis of a typical working set selection method for Sequential Minimal Optimization (SMO) algorithm along with the asymptotic behavior analysis of Support Vector Machines (SVM). The formula can delineate the tongue-shaped effective (C, γ) region in RBF SVC nearly perfectly as our experiments revealed. Our work may provide a basis for exploring the deep underpinnings that determine the shape of effective hyperparameter region in SVM, and may also invoke new ideas in hyperparameter tuning in SVM.