Ssvm: A smooth support vector machine for classification

Smoothing methods, extensively used for solving important math-ematical programming problems and applications, are applied here to generate and solve an unconstrained smooth reformulation of the support vector machine for pattern classication using a completely arbitrary kernel. We term such reformulation a smooth support vec-tor machine (SSVM). A fast Newton-Armijo algorithm for solving the SSVM converges globally and quadratically. Numerical results and comparisons are given to demonstrate the eectiveness and speed of the algorithm. On six publicly available datasets, tenfold cross vali-dation correctness of SSVM was the highest compared with four other methods as well as the fastest. On larger problems, SSVM was compa-rable or faster than SVMlight [17], SOR [23] and SMO [27]. SSVM can also generate a highly nonlinear separating surface such as a checker-board.