On the working set selection in gradient projection-based decomposition techniques for support vector machines

This work deals with special decomposition techniques for the large quadratic program arising in training support vector machines. These approaches split the problem into a sequence of quadratic programming (QP) subproblems which can be solved by efficient gradient projection methods recently proposed. Owing to the ability of decomposing the problem into much larger subproblems than standard decomposition packages, these techniques show promising performance and are well suited for parallelization. Here, we discuss a crucial aspect for their effectiveness: the selection of the working set; that is, the index set of the variables to be optimized at each step through the QP subproblem. We analyze the most popular working set selections and develop a new selection strategy that improves the convergence rate of the decomposition schemes based on large sized working sets. The effectiveness of the proposed strategy within the gradient projection-based decomposition techniques is shown by numerical experiments on large benchmark problems, both in serial and in parallel environments.