Angle-Based Cost-Sensitive Multicategory Classification
This work addresses cost-sensitive classification for multicategory problems, which is important for real-world applications but remains challenging, though it is incremental in building on existing boosting methods.
The paper tackles multicategory classification with varying misclassification costs by proposing an angle-based cost-sensitive framework that avoids the sum-to-zero constraint, reducing computational complexity and leading to competitive performance in numerical experiments.
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.