SSVM: A Amooth Support Vector Machine for Classification

Abstract

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 classi cation 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 e ectiveness 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.