Statistics and Its Interface
Volume 2 (2009)
Pages: 349 – 360
Boosting has been a very successful technique for solving the two-class classification problem. In going from two-class to multi-class classification, most algorithms have been restricted to reducing the multi-class classification problem to multiple two-class problems. In this paper, we develop a new algorithm that directly extends the AdaBoost algorithm to the multi-class case without reducing it to multiple two-class problems. We show that the proposed multi-class AdaBoost algorithm is equivalent to a forward stagewise additive modeling algorithm that minimizes a novel exponential loss for multi-class classification. Furthermore, we show that the exponential loss is a member of a class of Fisher-consistent loss functions for multi-class classification. As shown in the paper, the new algorithm is extremely easy to implement and is highly competitive in terms of misclassification error rate.
boosting, exponential loss, multi-class classification, stagewise modeling
2010 Mathematics Subject Classification