Laplacian smooth twin support vector machine for semi-supervised classification

Laplacian twin support vector machine (Lap-TSVM) is a state-of-the-art nonparallel-planes semi-supervised classifier. It tries to exploit the geometrical information embedded in unlabeled data to boost its generalization ability. However, Lap-TSVM may endure heavy burden in training procedure since it needs to solve two quadratic programming problems (QPPs) with the matrix "inversion'' operation. In order to enhance the performance of Lap-TSVM, this paper presents a new formulation of Lap-TSVM, termed as Lap-STSVM. Rather than solving two QPPs in dual space, firstly, we convert the primal constrained QPPs of Lap-TSVM into unconstrained minimization problems (UMPs). Afterwards, a smooth technique is introduced to make these UMPs twice differentiable. At last, a fast Newton-Armijo algorithm is designed to solve the UMPs in Lap-STSVM. Experimental evaluation on both artificial and real-world datasets demonstrate the benefits of the proposed approach.