The twin support vector machine and its extensions have made great achievements in dealing with binary classification problems. However, it suffers from difficulties in effective solution of multi-classification and fast model selection. This work devotes to the fast regularization parameter tuning algorithm for the twin multi-class support vector machine. Specifically, a novel sample data set partition strategy is first adopted, which is the basis for the model construction. Then, combining the linear equations and block matrix theory, the Lagrangian multipliers are proved to be piecewise linear w.r.t. the regularization parameters, so that the regularization parameters are continuously updated by only solving the break points. Next, Lagrangian multipliers are proved to be 1 as the regularization parameter approaches infinity, thus, a simple yet effective initialization algorithm is devised. Finally, eight kinds of events are defined to seek for the starting event for the next iteration. Extensive experimental results on nine UCI data sets show that the proposed method can achieve comparable classification performance without solving any quadratic programming problem.

翻译：孪生支持向量机及其扩展在解决二分类问题方面取得了显著成就。然而，它在有效处理多分类问题和快速模型选择方面存在困难。本文致力于研究孪生多类支持向量机的快速正则化参数调优算法。具体而言，首先采用了一种新颖的样本数据集划分策略，这是模型构建的基础。然后，结合线性方程组和分块矩阵理论，证明了拉格朗日乘子相对于正则化参数是分段线性的，从而仅通过求解断点即可连续更新正则化参数。接着，证明了当正则化参数趋近无穷大时，拉格朗日乘子为1，因此设计了一种简单有效的初始化算法。最后，定义了八种事件类型以寻找下一次迭代的起始事件。在九个UCI数据集上的大量实验结果表明，所提方法无需求解任何二次规划问题即可达到可比的分类性能。