  In this paper we measured the stability of stochastic gradient method (SGM)
for learning an approximated Fourier primal support vector machine. The
stability of an algorithm is considered by measuring the generalization error
in terms of the absolute difference between the test and the training error.
Our problem is to learn an approximated kernel function using random Fourier
features for a binary classification problem via online convex optimization
settings. For a convex, Lipschitz continuous and smooth loss function, given
reasonable number of iterations stochastic gradient method is stable. We showed
that with a high probability SGM generalizes well for an approximated kernel
under given assumptions.We empirically verified the theoretical findings for
different parameters using several data sets.
