Robust multicategory support vector machines using difference convex algorithm

• 成果类型: Article
• 署名作者: Zhang, Chong; Minh Pham; Fu, Sheng; Liu, Yufeng
• 署名单位: University of Waterloo; University of Virginia; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-017-1209-5
• 发表日期: 2018
• 页码: 277-305
• 关键词: Classification; models; svm

摘要

The support vector machine (SVM) is one of the most popular classification methods in the machine learning literature. Binary SVM methods have been extensively studied, and have achieved many successes in various disciplines. However, generalization to multicategory SVM (MSVM) methods can be very challenging. Many existing methods estimate k functions for k classes with an explicit sum-to-zero constraint. It was shown recently that such a formulation can be suboptimal. Moreover, many existing MSVMs are not Fisher consistent, or do not take into account the effect of outliers. In this paper, we focus on classification in the angle-based framework, which is free of the explicit sum-to-zero constraint, hence more efficient, and propose two robust MSVM methods using truncated hinge loss functions. We show that our new classifiers can enjoy Fisher consistency, and simultaneously alleviate the impact of outliers to achieve more stable classification performance. To implement our proposed classifiers, we employ the difference convex algorithm for efficient computation. Theoretical and numerical results obtained indicate that for problems with potential outliers, our robust angle-based MSVMs can be very competitive among existing methods.