A direct formulation for totally-corrective multi-class boosting

Boosting combines a set of moderately accurate weak classifiers to form a highly accurate predictor. Compared with binary boosting classification, multi-class boosting received less attention. We propose a novel multi-class boosting formulation here. Unlike most previous multi-class boosting algorithms which decompose a multi-boost problem into multiple independent binary boosting problems, we formulate a direct optimization method for training multi-class boosting. Moreover, by explicitly deriving the La-grange dual of the formulated primal optimization problem, we design totally-corrective boosting using the column generation technique in convex optimization. At each iteration, all weak classifiers' weights are updated. Our experiments on various data sets demonstrate that our direct multi-class boosting achieves competitive test accuracy compared with state-of-the-art multi-class boosting in the literature.