A support vector approach based on penalty function method

Support vector machine (SVM) models are usually trained by solving the dual of a quadratic programming, which is time consuming. Using the idea of penalty function method from optimization theory, this paper combines the objective function and the constraints in the dual, obtaining an unconstrained optimization problem, which could be solved by a generalized Newton method, yielding an approximate solution to the original model. Extensive experiments on pattern classification were conducted, and compared to the quadratic programming-based models, the proposed approach is much more computationally efficient (tens to hundreds of times faster) and yields similar performance in terms of receiver operating characteristic curve. Furthermore, the proposed method and quadratic programming-based models extract almost the same set of support vectors.