A class of semi-supervised support vector machines by DC programming
This paper investigate a class of semi-supervised support vector machines (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\text{ S }^3\mathrm{VMs}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mspace width="4.pt"/> <mtext>S</mtext> <msup> <mspace width="4.pt"/> <mn>3</mn> </msup> <mi mathvariant="normal">VMs</mi> </mrow> </math> </EquationSource> </InlineEquation>) with arbitrary norm. A general framework for the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$\text{ S }^3\mathrm{VMs}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mspace width="4.pt"/> <mtext>S</mtext> <msup> <mspace width="4.pt"/> <mn>3</mn> </msup> <mi mathvariant="normal">VMs</mi> </mrow> </math> </EquationSource> </InlineEquation> 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 <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$\text{ S }^3\mathrm{VMs}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mspace width="4.pt"/> <mtext>S</mtext> <msup> <mspace width="4.pt"/> <mn>3</mn> </msup> <mi mathvariant="normal">VMs</mi> </mrow> </math> </EquationSource> </InlineEquation> 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 <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$\text{ S }^3\mathrm{VM}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mspace width="4.pt"/> <mtext>S</mtext> <msup> <mspace width="4.pt"/> <mn>3</mn> </msup> <mi mathvariant="normal">VM</mi> </mrow> </math> </EquationSource> </InlineEquation> methods. Copyright Springer-Verlag Berlin Heidelberg 2013
