Quintic spline smooth semi-supervised support vector classification machine

Abstract

A semi-supervised vector machine is a relatively new learning method using both labeled and unlabeled data in classification. Since the objective function of the model for an unstrained semi-supervised vector machine is not smooth, many fast optimization algorithms cannot be applied to solve the model. In order to overcome the difficulty of dealing with non-smooth objective functions, new methods that can solve the semi-supervised vector machine with desired classification accuracy are in great demand. A quintic spline function with three-times differentiability at the origin is constructed by a general three-moment method, which can be used to approximate the symmetric hinge loss function. The approximate accuracy of the quintic spline function is estimated. Moreover, a quintic spline smooth semi-support vector machine is obtained and the convergence accuracy of the smooth model to the non-smooth one is analyzed. Three experiments are performed to test the efficiency of the model. The experimental results show that the new model outperforms other smooth models, in terms of classification performance. Furthermore, the new model is not sensitive to the increasing number of the labeled samples, which means that the new model is more efficient.