Determination of global minima of some common validation functions in support vector machine

Tuning of the regularization parameter C is a well-known process in the implementation of a support vector machine (SVM) classifier. Such a tuning process uses an appropriate validation function whose value, evaluated over a validation set, has to be optimized for the determination of the optimal C. Unfortunately, most common validation functions are not smooth functions of C. This brief presents a method for obtaining the global optimal solution of these non-smooth validation functions. The method is guaranteed to find the global optimum and relies on the regularization solution path of SVM over a range of C values. When the solution path is available, the computation needed is minimal.