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The class types are exchangeably described by and in this article when we talk about the imbalanced data problem. Define is the positive or minority class and is the negative or majority class. Let be a binary training dataset for a classification problem, where, in which is a subset of -dimensional vector space, and the response indicating two classes.

IntroductionĬlassification is one of the most important tasks in the machine learning and statistical field. Several numeric studies are listed finally to support our proposed algorithm. Besides, a way to determine the cost parameter value by the statistical analysis is introduced. We show that our proposed algorithm in the machine learning field is identical to the Product of Experts (PoE) model in the statistics field. Second, a statistical approach to prove the AdaImC algorithm is proposed to verify the inner relationship between the cost parameters. We name our specific one, the “AdaImC algorithm,” which is typically appliable to solve the imbalanced data classification problem with theoretic proof. First, we summarize the popular cost-sensitive boosting algorithms in the literature and propose a generally comprehensive form. To complete the cost-sensitive AdaBoost algorithms’ framework, the present article has two main contributions. The algorithms are appended the cost-sensitive factors to focus on the high-cost and small-class samples, but they have no procedures to show the best place to add the cost factors and the cost factor value set. However, the most available cost-sensitive AdaBoost algorithms are heuristic approaches, which are improved from the standard AdaBoost algorithm by cost-sensitively adjusting the voting weight parameters of weak classifiers or the sample updating weight parameters without strict theoretic proof. The cost-sensitive AdaBoost algorithms are practical since the “boosting” property in AdaBoost can iteratively enhance the small class of the cost-sensitive learning to solve the imbalanced data issue. To address the imbalanced data problem in classification, the studies of the combination of AdaBoost, short for “Adaptive Boosting,” and cost-sensitive learning have shown convincing results in the literature.