One novel class of Bezier smooth semi-supervised support vector machines for classification

The semi-supervised support vector machine ((SVM)-V-3) for classification is introduced for dealing with quantities of unlabeled data in the real world. Labeled data are utilized to train the algorithm and then were adapted to classify the unlabeled data. However, this algorithm has several drawbacks, such as the non-smooth term of semi-supervised objective function negatively affects the classification precision. Moreover, it is required to endure heavy burden in solving two quadratic programming problems with inversion matrix operation. To cope with this problem, this article puts forward a novel class of Bezier smooth semi-supervised support vector machines ((BSVMs)-V-4), based on the approximation property of Bezier function to the non-smooth term. Because of this approximation, a fast quasi-Newton method for solving (BSVMs)-V-4 can be used to decrease the calculating time scale. This new kind of algorithm enhances the generalization and robustness of (SVM)-V-3 for nonlinear case as well. Further, to show how the (BSVMs)-V-4 can be practically implemented, experiments on synthetic, UCI dataset, USPS dataset, and large-scale NDC database are offered. The theoretical analysis and experiments comparisons clearly confirm the superiority of (BSVMs)-V-4 in both classification accuracy and calculating time.