SSVM: A smooth support vector machine for classification

Smoothing methods, extensively used for solving important mathematical prog ramming problems and applications, are applied here to generate and solve a n unconstrained smooth reformulation of the support vector machine for patt ern classification using a completely arbitrary kernel. We term such reform ulation a smooth support vector machine (SSVM). A fast Newton-Armijo algori thm for solving the SSVM converges globally and quadratically. Numerical re sults and comparisons are given to demonstrate the effectiveness and speed of the algorithm. On six publicly available datasets, tenfold cross validat ion correctness of SSVM was the highest compared with four other methods as well as the fastest. On larger problems, SSVM was comparable or faster tha n SVMlight (T. Joachims, in Advances in Kernel Methods-Support Vector Learn ing, MIT Press: Cambridge, MA, 1999), SOR (O.L. Mangasarian and David R. Mu sicant, IEEE Transactions on Neural Networks, vol. 10, pp. 1032-1037, 1999) and SMO (J. Platt, in Advances in Kernel Methods-Support Vector Learning, MIT Press: Cambridge, MA, 1999). SSVM can also generate a highly nonlinear separating surface such as a checkerboard.