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

Abstract

This paper investigate a class of semi-supervised support vector machines ( $$\text{ S }^3\mathrm{VMs}$$ S 3 VMs ) with arbitrary norm. A general framework for the $$\text{ S }^3\mathrm{VMs}$$ S 3 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 $$\text{ S }^3\mathrm{VMs}$$ S 3 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 $$\text{ S }^3\mathrm{VM}$$ S 3 VM methods.