Multicategory Angle-Based Large Margin Classification

• Activity Number: 166
• Type: Topic Contributed
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Chong Zhang*+ and Yufeng Liu
• Companies: UNC-CH and The University of North Carolina
• Keywords: Large Margin ; Multiclass ; Simplex

Abstract

Large margin classifiers are popular classification techniques, and have been successfully applied in many applications. Despite success of binary large margin classifiers, extensions to multicategory problems are challenging. Among existing simultaneous multicategory extensions, the common one is to learn k different functions for a k class problem together with a sum-to-zero constraint on the functions. Such a formulation can be inefficient. In this paper, we propose a new Multicategory Angle based large margin Classification (MAC) technique. MAC associates different classes with vertices of a standard simplex. The prediction rule is to assign the class label that corresponds to the vertex whose angle with respect to the classification function is the smallest. All binary large margin classifiers can be naturally generalized to simultaneous multicategory classifiers through the MAC structure. MAC is free of the sum-to-zero constraint, and consequently enjoys more efficient computation. Theoretical results of MAC have been obtained. Our numerical studies suggest that the proposed MAC is very competitive in terms of classification accuracy, as well as the computational efficiency.