A class of semi-supervised support vector machines by DC programming

This paper investigate a class of semi-supervised support vector machines ( $\text{ S }^3\mathrm{VMs}$ ) with arbitrary norm. A general framework for the $\text{ S }^3\mathrm{VMs}$ was first constructed based on a robust DC (Difference of Convex functions) program. With different DC decompositions, DC optimization formulations for the linear and nonlinear $\text{ S }^3\mathrm{VMs}$ are investigated. The resulting DC optimization algorithms (DCA) only require solving simple linear program or convex quadratic program at each iteration, and converge to a critical point after a finite number of iterations. The effectiveness of proposed algorithms are demonstrated on some UCI databases and licorice seed near-infrared spectroscopy data. Moreover, numerical results show that the proposed algorithms offer competitive performances to the existing $\text{ S }^3\mathrm{VM}$ methods.