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 |
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Pages (from-to) | 67-81 |
Number of pages | 15 |
Journal | Biometrika |
Volume | 104 |
Issue number | 1 |
DOIs | |
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