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

被引：31

作者：

Shin, Seung Jun ^{[1
]}

Wu, Yichao ^{[2
]}

Zhang, Hao Helen ^{[3
]}

Liu, Yufeng ^{[4
]}

机构：

[1] Korea Univ, Dept Stat, Seoul 02841, South Korea

[2] North Carolina State Univ, Dept Stat, 2311 Stinson Dr,Campus Box 8203, Raleigh, NC 27695 USA

[3] Univ Arizona, Dept Math, 617 North Santa Rita Ave,POB 210089, Tucson, AZ 85721 USA

[4] Univ North Carolina Chapel Hill, Dept Stat & Operat Res, 354 Hanes Hall, Chapel Hill, NC 27599 USA

来源：

BIOMETRIKA | 2017年 / 104卷 / 01期

基金：

新加坡国家研究基金会; 美国国家卫生研究院; 美国国家科学基金会;

关键词：

Fisher consistency; Hyperplane alignment; Reproducing kernel Hilbert space; Weighted support vector machine; SLICED INVERSE REGRESSION; CENTRAL SUBSPACE; HESSIAN DIRECTIONS;

D O I：

10.1093/biomet/asw057

中图分类号：

Q [生物科学];

学科分类号：

07 ; 0710 ; 09 ;

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.

引用

页码：67 / 81

页数：15

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