Study on -SVM for Classification Optimization Problem without Bias

In the high-dimensional space, the classification hyperplane tends to pass through the origin and bias (b) is not need. To study whether -SVM for classification needs (b), dual optimization formulation of-SVM without (b) is proposed and the corresponding method of solving the optimization formulation is presented. The dual optimization formulation is transformed into equality constraint sub-optimization formulation by the active set strategy in this method, then the sub-optimization formulation is transformed into the linear equation by lagrange multiplier method. The experimental results show that the existence of (b) would reduce the generalization ability of-SVM and-SVM can only obtain the sub-optimal solution of-SVM without b.