A new conic approach to semisupervised support vector machines (Q1793456)

Summary: We propose a completely positive programming reformulation of the 2-norm soft margin \(\mathrm{S}^3 \mathrm{VM}\) model. Then, we construct a sequence of computable cones of nonnegative quadratic forms over a union of second-order cones to approximate the underlying completely positive cone. An \(\epsilon\)-optimal solution can be found in finite iterations using semidefinite programming techniques by our method. Moreover, in order to obtain a good lower bound efficiently, an adaptive scheme is adopted in our approximation algorithm. The numerical results show that the proposed algorithm can achieve more accurate classifications than other well-known conic relaxations of semisupervised support vector machine models in the literature.