Multi-parameter safe screening rule for hinge-optimal margin distribution machine

Optimal margin distribution machine (ODM) is an efficient algorithm for classification problems. ODM attempts to optimize the margin distribution by maximizing the margin mean and minimizing the margin variance simultaneously, so it can achieve a better generalization performance. However, it is relatively time-consuming for large-scale problems. In this paper, we propose a hinge loss-based optimal margin distribution machine (Hinge-ODM), which derives a simplified substitute formulation. It can speed up the solving process without affecting the optimal accuracy obviously. Besides, inspired by its sparse solution, we put forward a multi-parameter safe screening rule for Hinge-ODM, called MSSR-Hinge-ODM. Based on the MSSR, most non-support vectors can be identified and deleted beforehand so the scale of dual problem will be greatly reduced. Moreover, our MSSR is safe, that is, it can get the exactly same optimal solutions as the original one. Furthermore, a fast algorithm DCDM is introduced to further solve the reduced Hinge-ODM. Finally, we integrate the MSSR into grid search method to accelerate the whole training process. Experimental results on twenty data sets demonstrate the superiority of the proposed methods.