  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.
