Many real-world classification problems come with costs which can vary for different types of misclassification. It is thus important to develop cost-sensitive classifiers which minimize the total misclassification cost. Although binary cost-sensitive classifiers have been well-studied, solving multicategory classification problems is still challenging. A popular approach to address this issue is to construct K classification functions for a K-class problem and remove the redundancy by imposing a sum-to-zero constraint. However, such method usually results in higher computational complexity and inefficient algorithms. In this paper, we propose a novel angle-based cost-sensitive classification framework for multicategory classification without the sum-to-zero constraint. Loss functions that included in the angle-based cost-sensitive classification framework are further justified to be Fisher consistent. To show the usefulness of the framework, two cost-sensitive multicategory boosting algorithms are derived as concrete instances. Numerical experiments demonstrate that proposed boosting algorithms yield competitive classification performances against other existing boosting approaches.

中文翻译：

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基于角度的成本敏感多类别分类

许多现实世界的分类问题都伴随着成本，这些成本可能因不同类型的错误分类而异。因此，重要的是开发成本敏感的分类器，以最大限度地减少总错误分类成本。尽管二元成本敏感分类器已得到充分研究，但解决多类别分类问题仍然具有挑战性。解决此问题的一种流行方法是为 K 类问题构建 K 个分类函数，并通过施加总和为零的约束来消除冗余。然而，这种方法通常会导致更高的计算复杂度和低效的算法。在本文中，我们提出了一种新的基于角度的成本敏感分类框架，用于没有总和为零约束的多类别分类。包含在基于角度的成本敏感分类框架中的损失函数被进一步证明是 Fisher 一致的。为了展示该框架的实用性，我们导出了两个成本敏感的多类别提升算法作为具体实例。数值实验表明，与其他现有的提升方法相比，所提出的提升算法产生了具有竞争力的分类性能。