Linear programming ν-nonparallel support vector machine and its application in vehicle recognition

In this paper, based on the nonparallel hyperplane classifier, ν-nonparallel support vector machine (ν-NPSVM), we proposed its linear programming formulation, termed as ν-LPNPSVM. ν-NPSVM which has been proved superior to the twin support vector machines (TWSVMs), is parameterized by the quantity ν to let ones effectively control the number of support vectors. Compared with the quadratic programming problem of ν-NPSVM, the 1-norm regularization term is introduced to ν-LPNPSVM to make it to be linear programming problem which can be solved fastly and easily. We also introduce kernel functions directly into the formulation for the nonlinear case. The numerical experiments on lots of data sets verify that our ν-LPNPSVM is superior to TWSVMs and faster than standard NPSVMs. We also apply this new method to the vehicle recognition problem and justify its efficiency.