A general cubic spline smooth semi-supervised support vector machine

This article is focused on the non-smooth problem of the semi-supervised support vector machine optimization model. A smooth semi-supervised support vector machine model was established. A general cubic spline function with 2 times differentiable at zero point was deduced by a general three-moment method and was used to approach the non-smooth part in the semi-supervised support vector machine. A new smooth semi-supervised support vector with 1 time differentiable based on the general cubic spline function was constructed, and thus a lot of fast optimization algorithms could be applied to solve the smooth semi-supervised vector machine model. The approximation accuracy of the general cubic spline function to the symmetric hinge loss function was analyzed, and the convergence accuracy of the new model was proved. Numerical experiments show that the new model has a better classification result.