  Stochastic gradient descent algorithm has been successfully applied on
support vector machines (called PEGASOS) for many classification problems. In
this paper, stochastic gradient descent algorithm is investigated to twin
support vector machines for classification. Compared with PEGASOS, the proposed
stochastic gradient twin support vector machines (SGTSVM) is insensitive on
stochastic sampling for stochastic gradient descent algorithm. In theory, we
prove the convergence of SGTSVM instead of almost sure convergence of PEGASOS.
For uniformly sampling, the approximation between SGTSVM and twin support
vector machines is also given, while PEGASOS only has an opportunity to obtain
an approximation of support vector machines. In addition, the nonlinear SGTSVM
is derived directly from its linear case. Experimental results on both
artificial datasets and large scale problems show the stable performance of
SGTSVM with a fast learning speed.
