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 journalArticle

4 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 languageEnglish
Pages (from-to)67-81
Number of pages15
JournalBiometrika
Volume104
Issue number1
DOIs
Publication statusPublished - 2017 Mar 1

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Keywords

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

ASJC Scopus subject areas

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

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