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:双支持矢量机及其扩展在处理二进制分类问题方面取得了巨大成就。 但是, 它在有效解决多级分类和快速模型选择方面遇到困难。 这项工作致力于双级支持矢量机快速正规化参数调算算法。 具体地说, 首先采用了新型的样本数据集分割战略, 这是模型构建的基础。 然后, 结合线性方程式和块状矩阵理论, Lagrangian 乘数被证明是小写线性线性( w.r.t.) 正规化参数, 以便仅通过解决断点来不断更新正规化参数。 下一步, Lagrangian 乘数被证明为1, 作为正规化参数接近无限性, 从而设计了一个简单而有效的初始化算法。 最后, 确定了八类事件, 以寻找下次迭代的起始事件。 九个 UCI 数据集的广泛实验结果显示, 拟议的方法可以在不解决任何二次线性编程问题的情况下实现可比的分类性工作。