Large-margin classifiers are powerful techniques for classification problems. Although binary large-margin classifiers are heavily studied, multicategory problems are more complicated and challenging. A common approach is to construct k different decision functions for a k-class problem with a sum-to-zero constraint. However, such a constraint can be inefficient. Moreover, many large-margin classifiers can be sensitive to outliers in the training sample. In this article, we use the angle-based classification framework to avoid the explicit sum-to-zero constraint, and we propose two adaptively weighted large-margin classification techniques. Our new methods are Fisher consistent and more robust against outliers under suitable conditions. Numerical experiments further indicate that our methods give competitive and stable performance when compared with existing approaches.

中文翻译：

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自适应加权大边距角分类器

大边界分类器是解决分类问题的强大技术。尽管对二元大边界分类器进行了大量研究，但多类别问题更加复杂和具有挑战性。一种常见的方法是为具有总和为零约束的 k 类问题构造 k 个不同的决策函数。然而，这样的约束可能是低效的。此外，许多大边界分类器可能对训练样本中的异常值敏感。在本文中，我们使用基于角度的分类框架来避免显式和为零的约束，并且我们提出了两种自适应加权的大边界分类技术。我们的新方法是 Fisher 一致的，并且在合适的条件下对异常值更加稳健。