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An uncertain support vector machine with imprecise observations

Author

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  • Zhongfeng Qin

    (Beihang University
    Key Laboratory of Complex System Analysis, Management and Decision (Beihang University), Ministry of Education)

  • Qiqi Li

    (Beihang University)

Abstract

Support vector machines have been widely applied in binary classification, which are constructed based on crisp data. However, the data obtained in practice are sometimes imprecise, in which classical support vector machines fail in these situations. In order to handle such cases, this paper employs uncertain variables to describe imprecise observations and further proposes a hard margin uncertain support vector machine for the problem with imprecise observations. Specifically, we first define the distance from an uncertain vector to a hyperplane and give the concept of a linearly α-separable data set. Then, based on maximum margin criterion, we propose an uncertain support vector machine for the linearly α-separable data set, and derive the corresponding crisp equivalent forms. New observations can be classified through the optimal hyperplane derived from the model. Finally, a numerical example is given to illustrate the uncertain support vector machine.

Suggested Citation

  • Zhongfeng Qin & Qiqi Li, 2023. "An uncertain support vector machine with imprecise observations," Fuzzy Optimization and Decision Making, Springer, vol. 22(4), pages 611-629, December.
    • Handle: RePEc:spr:fuzodm:v:22:y:2023:i:4:d:10.1007_s10700-022-09404-0
    DOI: 10.1007/s10700-022-09404-0
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    References listed on IDEAS

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    1. Yang Liu & Baoding Liu, 2022. "Residual analysis and parameter estimation of uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 21(4), pages 513-530, December.
    2. Zhe Liu & Ying Yang, 2020. "Least absolute deviations estimation for uncertain regression with imprecise observations," Fuzzy Optimization and Decision Making, Springer, vol. 19(1), pages 33-52, March.
    3. Qin, Zhongfeng, 2015. "Mean-variance model for portfolio optimization problem in the simultaneous presence of random and uncertain returns," European Journal of Operational Research, Elsevier, vol. 245(2), pages 480-488.
    4. Mingxuan Zhao & Yuhan Liu & Dan A. Ralescu & Jian Zhou, 2018. "The covariance of uncertain variables: definition and calculation formulae," Fuzzy Optimization and Decision Making, Springer, vol. 17(2), pages 211-232, June.
    5. Xiangfeng Yang & Baoding Liu, 2019. "Uncertain time series analysis with imprecise observations," Fuzzy Optimization and Decision Making, Springer, vol. 18(3), pages 263-278, September.
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    Cited by:

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