Within the framework of AdaBoost.MH, we propose to train vector-valued decision trees to optimize the multi-class edge without reducing the multi-class problem to $K$ binary one-against-all classifications. The key element of the method is a vector-valued decision stump, factorized into an input-independent vector of length $K$ and label-independent scalar classifier. At inner tree nodes, the label-dependent vector is discarded and the binary classifier can be used for partitioning the input space into two regions. The algorithm retains the conceptual elegance, power, and computational efficiency of binary AdaBoost. In experiments it is on par with support vector machines and with the best existing multi-class boosting algorithm AOSOLogitBoost, and it is significantly better than other known implementations of AdaBoost.MH.

本文提出了基于AdaBoost.MH框架的向量决策树方法，通过使用向量值决策树进行多类边缘优化而不是将多类问题规约为$K$个一对多分类，其中关键要素是由长度为$K$的与标签无关的标量分类器分解出来的与输入无关的向量值决策树桩，在这种方法下，二元分类器可以用于将输入空间分成两个区域，该算法保留了二进制AdaBoost的概念优雅性、强大性和计算效率，在实验中与支持向量机和现有最佳的多类提升算法AOSOLogitBoost旗鼓相当，而且明显优于其他已知的AdaBoost.MH实现。

AdaBoost.MH的回归：多类别Hamming树