Adjustable entropy funtion method for misclassification minimization problems

Misclassification minimization problem is a fundamental problem of support vector machines. It can be stated by a way of minimizing the sum of violations of misclassified points, generally, its objective function is non-differentiable. In order to solve this problem, commonly, ones either use the Sigmoid functions (or a concave functions) sequence to approximate the step function, while the problem is converted into a constrained linear programming model, or use differentiable functions sequence to approximate non-differential objective function by the successive iterative optimization algorithm. But one of serious deficiency of these known algorithms is that the phenomenon of ill-conditioned matrix and data overflow occurs in the numerical computing. To overcome the drawbacks mentioned above, a new differentiable functions sequence constructed by the adjustable entropy function method proposed in [14], is adopted to approximate the non-differentiable objective function of the primal problem, a new optimization algorithm is designed to solve this problem. Further, the stop criterion of above adjustable entropy function method is improved and another new optimization algorithm is given consequently. The experimental results validate the accuracy and efficiency of the proposed algorithms for solving the problem, the classification accuracy of two new algorithms is almost accordant, but the computational efficiency of the last one is faster than the first one.