  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.
