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.