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

Author

Listed:
  • Seung Jun Shin
  • Yichao Wu
  • Hao Helen Zhang
  • Yufeng Liu

Abstract

SUMMARY 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.

Suggested Citation

  • Seung Jun Shin & Yichao Wu & Hao Helen Zhang & Yufeng Liu, 2017. "Principal weighted support vector machines for sufficient dimension reduction in binary classification," Biometrika, Biometrika Trust, vol. 104(1), pages 67-81.
    • Handle: RePEc:oup:biomet:v:104:y:2017:i:1:p:67-81.
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    File URL: http://hdl.handle.net/10.1093/biomet/asw057
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    References listed on IDEAS

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    1. Seung Jun Shin & Yichao Wu & Hao Helen Zhang & Yufeng Liu, 2014. "Probability-enhanced sufficient dimension reduction for binary classification," Biometrics, The International Biometric Society, vol. 70(3), pages 546-555, September.
    2. R. Dennis Cook & Liqiang Ni, 2006. "Using intraslice covariances for improved estimation of the central subspace in regression," Biometrika, Biometrika Trust, vol. 93(1), pages 65-74, March.
    3. Bura, E. & Pfeiffer, R., 2008. "On the distribution of the left singular vectors of a random matrix and its applications," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2275-2280, October.
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    Cited by:

    1. Jang, Hyun Jung & Shin, Seung Jun & Artemiou, Andreas, 2023. "Principal weighted least square support vector machine: An online dimension-reduction tool for binary classification," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    2. Li, Junlan & Wang, Tao, 2021. "Dimension reduction in binary response regression: A joint modeling approach," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    3. Xuehu Zhu & Rongzhu Zhao & Dan Zeng & Qian Zhao & Jun Zhang, 2024. "Dimension reduction-based adaptive-to-model semi-supervised classification," Statistical Papers, Springer, vol. 65(7), pages 4631-4675, September.
    4. Qin Wang & Yuan Xue, 2023. "A structured covariance ensemble for sufficient dimension reduction," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(3), pages 777-800, September.
    5. Hayley Randall & Andreas Artemiou & Xingye Qiao, 2021. "Sufficient dimension reduction based on distance‐weighted discrimination," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(4), pages 1186-1211, December.
    6. Lu Li & Niwen Zhou & Lixing Zhu, 2022. "Outcome regression-based estimation of conditional average treatment effect," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(5), pages 987-1041, October.
    7. Pircalabelu, Eugen & Artemiou, Andreas, 2021. "Graph informed sliced inverse regression," Computational Statistics & Data Analysis, Elsevier, vol. 164(C).
    8. Pircalabelu, Eugen & Artemiou, Andreas, 2020. "The LassoPSVM approach for sufficient dimension reduction using principal projections," LIDAM Discussion Papers ISBA 2020008, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. Wei Luo, 2022. "On efficient dimension reduction with respect to the interaction between two response variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 269-294, April.

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