Twin Support Vector Machine in Linear Programs

This paper propose a new algorithm, termed as LPTWSVM, for binary classification problem by seeking two nonparallel hyperplanes which is an improved method for TWSVM. We improve the recently proposed ITSVM and develop Generalized ITSVM. A linear function is chosen in the object function of Generalized ITSVM which leads to the primal problems of LPTWSVM. Comparing with TWSVM, a 1-norm regularization term is introduced to the objective function to implement structural risk minimization and the quadratic programming problems are changed to linear programming problems which can be solved fast and easily. Then we do not need to compute the large inverse matrices or use any optimization trick in solving our linear programs and the dual problems are unnecessary in the paper. We can introduce kernel function directly into nonlinear case which overcome the serious drawback of TWSVM. The numerical experiments verify that our LPTWSVM is very effective