A proximal quadratic surface support vector machine for semi-supervised binary classification

Semi-supervised support vector machine is a popular method in the research area of machine learning. Considering a large amount of unlabeled data points in real-life world, the semi-supervised support machine has the ability of good generalization for dealing with nonlinear classification problems. In this paper, a proximal quadratic surface support vector machine model is proposed for semi-supervised binary classification. The main advantage of our new model is that the proximal quadratic surfaces are constructed directly for nonlinear classification instead of using the kernel function, which avoids the tasks of choosing kernels and tuning their parameters. We reformulate this proposed model as an unconstrained mixed-integer quadratic programming problem. Semi-definite relaxation is then adopted, and a primal alternating direction method is further proposed for fast computation. We test the proposed method on some artificial and public benchmark data sets. Preliminary results indicate that our method outperforms some well-known methods for semi-supervised classification in terms of the efficiency and classifying accuracy.