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Many real-world classification problems come with costs which can vary fordifferent types of misclassification. It is thus important to developcost-sensitive classifiers which minimize the total misclassification cost.Although binary cost-sensitive classifiers have been well-studied, solvingmulticategory classification problems is still challenging. A popular approachto address this issue is to construct K classification functions for a K-classproblem and remove the redundancy by imposing a sum-to-zero constraint.However, such method usually results in higher computational complexity andinefficient algorithms. In this paper, we propose a novel angle-basedcost-sensitive classification framework for multicategory classificationwithout the sum-to-zero constraint. Loss functions that included in theangle-based cost-sensitive classification framework are further justified to beFisher consistent. To show the usefulness of the framework, two cost-sensitivemulticategory boosting algorithms are derived as concrete instances. Numericalexperiments demonstrate that proposed boosting algorithms yield competitiveclassification performances against other existing boosting approaches.

Angle-Based Cost-Sensitive Multicategory Classification