A New Model of Multi-class Support Vector Machine with Parameter v

A new model of multi-class support vector machine with parameter v (v-MC-SVM) is proposed firstly based on v-SVM. Existence of optimal solutions and dual problem of v-MC-SVM are also given. Because the constraints of v-MC-SVM are too complicated, one-class SVM problem is given by adding b
_m
to the objective function of v-MC-SVM and employing the Kesler's construction which simplify the original problem. The optimal solutions of one-class SVM problem are unchanged when its constraint e
^T
¿ ¿ v is replaced with e
^T
¿ = v. Numerical testing results show that the speed of v-MC-SVM algorithm is faster than that of QP-MC-SVM algorithm under the same accuracy rate.