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.