Abstract   Motivated by the fact that the  l   1  -penalty is piecewise linear, we proposed a ramp loss linear programming nonparallel support vector machine (ramp-LPNPSVM), in which the  l   1  -penalty is applied for the RNPSVM, for binary classification. Since the ramp loss has the piecewise linearity as well, ramp- LPNPSVM is a piecewise linear minimization problem and a local minimum can be effectively found by the Concave Convex Procedure and experimental results on benchmark datasets confirm the effectiveness of the proposed algorithm. Moreover, the  l   1  -penalty can enhance the sparsity.
['Dalian Liu', 'Dandan Chen', 'Yong Shi', 'Yingjie Tian']
Ramp Loss Linear Programming Nonparallel Support Vector Machine