Smooth Diagonal Weighted Newton Support Vector Machine

Based on diagonal weighted support vector machine, a smooth model with Newton algorithm is proposed and is called SDWNSVM for short. SDWNSVM introduces the entropy function to approximate the plus function of the slack in the diagonal weighted SVM and is thus different from traditional SSVM that treats a reformulation problem. SDWNSVM utilizes the dual technique to rewrite the objection function by the connotative relation between the primal and dual program, which induces an exact smooth program and differs from traditional SSVM that uses Lagrangian multipliers to roughly substitute for the hyperplane weight. SDWNSVM proves the equivalence between the obtained model and the original one and proposes Newton algorithm to figure out the optimal solution. Numerical experiments on UCI data demonstrate that SDWNSVM has higher accuracies and less iteration than existing methods.