一种基于指数损失函数的多类分类AdaBoost算法及其应用

 提出一种新的多类分类AdaBoost算法——使用多类分类指数损失函数的前向逐步叠加模型FSAMME（forward stagewise additive modeling using a multi class exponential loss function）。该算法是基于原始的两类分类AdaBoost算法归结为使用两类分类指数损失函数的前向逐步叠加模型的统计学观点，将两类分类的前向逐步叠加模型自然扩展到多类分类情况下得到的，并采用多类指数损失函数和前向逐步叠加模型对FSAMME进行了详细的理论证明。该算法大大降低对弱分类器的精度要求，只需每个弱分类器的精度比随机猜测好；算法简单明了，不用把多类问题转化为多个两类问题，而是直接求解多类分类问题，大大减小计算复杂度和计算量。通过对基准数据库的测试分类及航空发动机故障样本的诊断，结果表明:FSAMME算法一方面可达到较高的分类诊断准确率，其准确率明显高于AdaBoost.M1，略高于AdaBoost.MH；另一方面可大大减小计算成本，满足在线快速分类诊断的要求。

An AdaBoost Algorithm for Multi-class Classification Based on Exponential Loss Function and Its Application

A new AdaBoost algorithm for multi-class classification is presented,which is named FSAMME(forward stagewise additive modeling using a multi-class exponential loss function).Further on,the detailed theoretical justification for FSAMME using a novel multi-class exponential loss function and forward stage-wise additive modeling is provided.The proposed algorithm only requires the performance of each weak classifier to be better than random guessing(rather than 1/2) and directly solves the multi-class classification question instead of reducing the multi-class classification problem to multiple two-class problems.The practical applications in UCI repository and aeorengine faulty samples show that the proposed method has higher classification accuracy,which is evidently higher than that of AdaBoost.M1 is slightly higher than that of AdaBoost.MH,meanwhile the proposed method can enormously reduce the computation cost and meet the demand of online quick diagnosis.