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

Seung Jun Shin; Yichao Wu; Hao Helen Zhang; Yufeng Liu

doi:10.1093/biomet/asw057

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

Seung Jun Shin, Yichao Wu, Hao Helen Zhang, Yufeng Liu

Research output: Contribution to journal › Article › peer-review

33 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	67-81
Number of pages	15
Journal	Biometrika
Volume	104
Issue number	1
DOIs	https://doi.org/10.1093/biomet/asw057
Publication status	Published - 2017 Mar 1

Bibliographical note

Funding Information:
Our research is partially supported by the National Institutes of Health, the National Science Foundation and the National Research Foundation of Korea.

Publisher Copyright:
© 2017 Biometrika Trust.

Keywords

Fisher consistency
Hyperplane alignment
Reproducing kernel Hilbert space
Weighted support vector machine

ASJC Scopus subject areas

Statistics and Probability
General Mathematics
Agricultural and Biological Sciences (miscellaneous)
General Agricultural and Biological Sciences
Statistics, Probability and Uncertainty
Applied Mathematics

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AU - Wu, Yichao

AU - Zhang, Hao Helen

AU - Liu, Yufeng

N1 - Funding Information: Our research is partially supported by the National Institutes of Health, the National Science Foundation and the National Research Foundation of Korea. Publisher Copyright: © 2017 Biometrika Trust.

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N2 - 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.

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KW - Hyperplane alignment

KW - Reproducing kernel Hilbert space

KW - Weighted support vector machine

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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