Coincidence of the Solutions of the Modified Problem with the Original Problem of v-MC-SVM

Multi-class support vector machine with parameter v (v-MC-SVM)is a kind of machine learning method which is similar to QP-MC-SVM The constraints of v-MC-SVM and it's dual problem are too complicated By adding the term bm to the objective function of v-MC-SVM, the original problem was modified Then,by employing the Kesler's construction, the modified problem is simplified Efficient algorithms can be used to solve the simplified problem Numerical testing results show that v-MC-SVM has the same accuracy rate as QP-MC-SVM Basing on Lagrange function and KKT condition, this paper proves strictly that the solution of the modified problem is the solution of the original problem, which provides the muli-class SVM with theory bases.