Principal weighted support vector machines for sufficient dimension reduction in binary classification

• 成果类型: Article
• 署名作者: Shin, Seung Jun; Wu, Yichao; Zhang, Hao Helen; Liu, Yufeng
• 署名单位: Korea University; North Carolina State University; University of Arizona; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asw057
• 发表日期: 2017
• 页码: 6781
• 关键词: sliced inverse regression; central subspace; hessian directions

摘要

Sufficient dimension reduction is popular for reducing data dimensionality without stringent model assumptions. However, most existing methods may work poorly for binary classification. For example, sliced inverse regression (Li, 1991) can estimate at most one direction if the response is binary. In this paper we propose principal weighted support vector machines, a unified framework for linear and nonlinear sufficient dimension reduction in binary classification. Its asymptotic properties are studied, and an efficient computing algorithm is proposed. Numerical examples demonstrate its performance in binary classification.