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.

最优边距分配机（ODM）是一种有效的分类问题算法。ODM尝试通过同时最大化边际均值和最小化边际方差来优化边际分布，以便获得更好的泛化性能。但是，解决大规模问题相对耗时。在本文中，我们提出了一种基于铰链损耗的最优边距分配机（Hinge-ODM），该机推导了简化的替代公式。它可以加快求解过程，而不会明显影响最佳精度。此外，受其稀疏解决方案的启发，我们针对Hinge-ODM提出了多参数安全筛选规则，称为MSSR-Hinge-ODM。基于MSSR，可以预先识别和删除大多数非支持向量，从而大大降低了对偶问题的规模。而且，我们的MSSR是安全的，也就是说，它可以获得与原始解决方案完全相同的最佳解决方案。此外，引入了快速算法DCDM以进一步解决简化的Hinge-ODM。最后，我们将MSSR集成到网格搜索方法中，以加快整个训练过程。在二十个数据集上的实验结果证明了所提出方法的优越性。