Maximum margin of twin spheres support vector machine (MMTSSVM) is an efficient method for imbalanced data classification. As an extension to enhance noise insensitivity of MMTSSVM, MMTSSVM with pinball loss (Pin-MMTSM) has a good generalization performance. However, it is not efficient enough for large-scale data. Inspired by the sparse solution of SVMs, in this paper, we propose a safe accelerative approach to reduce the computational cost. Unlike the existing safe screening rules, where only one variable changes with the parameters. We utilize bound estimation-based to derive the upper and lower bounds of center and radius. With our approach, the inactive samples are discarded before solving the problem, thus it can reduce the computational cost. One important advantage of our approach is safety, i.e., we can obtain the same solution as solving original problem both in linear and non-linear cases. Moreover, it is obvious that our acceleration approach is independent of the solver. To further accelerate the computational speed, a decomposition method is employed. Experiments on three artificial datasets and twelve benchmark datasets clearly demonstrate the effectiveness of our approach. At last, we extend bound estimation-based method to $\nu$-SVM, theoretical analysis and experimental results both verify its feasibility and effectiveness.

双球支持向量机（MMTSSVM）的最大余量是一种不平衡数据分类的有效方法。作为增强MMTSSVM的噪声不敏感性的扩展，具有弹球损失的MMTSSVM（Pin-MMTSM）具有良好的泛化性能。但是，它对于大规模数据而言不够高效。受SVM稀疏解决方案的启发，本文提出了一种安全的加速方法来降低计算成本。与现有的安全筛选规则不同，在安全筛选规则中，只有一个变量随参数发生变化。我们利用基于边界的估计来导出中心和半径的上限和下限。使用我们的方法，在解决问题之前将不活动的样本丢弃，从而可以降低计算成本。我们的方法的一个重要优势是安全性，即 我们可以在线性和非线性情况下获得与解决原始问题相同的解决方案。此外，很明显，我们的加速方法与求解器无关。为了进一步加快计算速度，采用了分解方法。在三个人工数据集和十二个基准数据集上进行的实验清楚地证明了我们方法的有效性。最后，我们将基于边界估计的方法扩展到$\nu$-SVM，理论分析和实验结果均证明了其可行性和有效性。