一类不确定支持向量机问题的鲁棒可行性半径精确公式

肖彩云, 孙祥凯

系统科学与数学 ›› 2024, Vol. 44 ›› Issue (1) : 260-268.

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系统科学与数学 ›› 2024, Vol. 44 ›› Issue (1) : 260-268. DOI: 10.12341/jssms22400

一类不确定支持向量机问题的鲁棒可行性半径精确公式

    肖彩云, 孙祥凯
作者信息 +

An Exact Formula of Radius of Robust Feasibility for a Class of Uncertain Support Vector Machine Problems

    XIAO Caiyun, SUN Xiangkai
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文章历史 +

摘要

文章旨在研究一类不确定支持向量机问题的鲁棒可行性.首先借助鲁棒优化方法,引入该不确定支持向量机问题的鲁棒对等问题.随后给出鲁棒对等问题的重构优化问题.最后借助该重构问题和上图集,得到该不确定支持向量机问题的鲁棒可行性半径的精确计算公式.

Abstract

This paper is concerned with the robust feasibility for a class of support vector machine problems with uncertain data. Firstly, a robust counterpart problem of the uncertain support vector machine problem is introduced in terms of robust optimization. Then, a reformulation of the robust counterpart problem of the uncertain support vector machine problem is given. Finally, by using this reformulation and the so-called epigraphical set, an exact formula for the radius of robust feasibility of the uncertain support vector machine problem is obtained.

关键词

支持向量机问题 / 鲁棒优化 / 鲁棒可行性

Key words

Support vector machine problem / robust optimization / robust feasibility

引用本文

导出引用
肖彩云 , 孙祥凯. 一类不确定支持向量机问题的鲁棒可行性半径精确公式. 系统科学与数学, 2024, 44(1): 260-268. https://doi.org/10.12341/jssms22400
XIAO Caiyun , SUN Xiangkai. An Exact Formula of Radius of Robust Feasibility for a Class of Uncertain Support Vector Machine Problems. Journal of Systems Science and Mathematical Sciences, 2024, 44(1): 260-268 https://doi.org/10.12341/jssms22400
中图分类号: 90C17    90C20   

参考文献

[1] Vapnik V N. Statistical Learning Theory. New York:Wiley, 1998.
[2] Abe S. Support Vector Machines for Pattern Classification. New York:Springer, 2010.
[3] 周志华. 机器学习. 北京:清华大学出版社, 2016. (Zhou Z H. Machine Learning. Beijing:Tsinghua University Press, 2016.)
[4] Dunbar M, Murray J M, Cysiqued L A, et al. Simultaneous classification and feature selection via convex quadratic programming with application to HIV-associated neurocognitive disorder assessment. Eur. J. Oper. Res., 2010, 206:470-478.
[5] Xie J, Wang C. Using support vector machines with a novel hybrid feature selection method for diagnosis of erythemato-squamous diseases. Expert. Syst. Appl., 2011, 38:5809-5815.
[6] Li C H, Kuo B C, Lin C T, et al. A spatial-contextual support vector machine for remotely sensed image classification. IEEE Trans. Geosci. Remote Sens., 2012, 50:784-799.
[7] Wang X, Pardalos P M. A survey of support vector machines with uncertainties. Ann. Data. Sci., 2014, 1:293-309.
[8] Zendehboudi A, Baseer M A, Saidur R. Application of support vector machine models for forecasting solar and wind energy resources:A review. J. Clean. Prod., 2018, 199:272-285.
[9] 于静, 韩鲁青. 一种改进的求解支持向量机模型的坐标梯度下降算法. 系统科学与数学, 2018, 38(5):583-590. (Yu J, Han L Q. A coordinate gradient descent algorithm for support vector machines training. Journal of Systems Science and Mathematical Sciences, 2018, 38(5):583-590.)
[10] 李博, 孟志青, 朱爱花. 时态支持向量机模型在股票操纵模式发现上的研究. 系统科学与数学, 2023, 43(2):356-378. (Li B, Meng Z Q, Zhu A H. Research on temporal support vector machine model in the discovery of stock manipulation patterns. Journal of Systems Science and Mathematical Sciences, 2023, 43(2):356-378.)
[11] Jeyakumar V, Ormerod J, Womersley R S. Knowledge-based semidefinite linear programming classifiers. Optim. Meth. Soft., 2006, 21:693-706.
[12] Li G Y, Jeyakumar V, Lee G M. Robust conjugate duality for convex optimization under uncertainty with application to data classification. Nonlinear Anal., 2011, 74:2327-2341.
[13] Fan N, Elham S, Pardalos P M. Robust support vector machines with polyhedral uncertainty of the input data. Learning and Intelligent Optimization, Eds. by Pardalos P M, Resende M G C, Vogiatzis C, et al. Berlin:Springer, 2014, 291-305.
[14] Jeyakumar V, Li G, Suthaharan S. Support vector machine classifiers with uncertain knowledge sets via robust optimization. Optimization, 2014, 63:1099-1116.
[15] Wang X, Fan N, Pardalos P M. Stochastic subgradient descent method for large-scale robust chance-constrained support vector machines. Optim. Lett., 2017, 11:1013-1024.
[16] Woolnough D, Jeyakumar N, Li G, et al. Robust optimization and data classification for characterization of Huntington disease onset via duality methods. J. Optim. Theory. Appl., 2022, 193:649-675.
[17] Ben-Tal A, Nemirovski A. Robust convex optimization-methodology and applications. Math Program Ser. B, 2002, 92:453-480.
[18] Ben-Tal A, Ghaoui L E, Nemirovski A. Robust Optimization. Princeton:Princeton University Press, 2009.
[19] 莫晓庆, 孙祥凯. 不确定非凸半无限优化问题的Mond-Weir型鲁棒逼近对偶性. 系统科学与数学, 2022, 42(5):1190-1199. (Mo X Q, Sun X K. Mond-Weir type robust approximate duality for nonconvex semi-Infinite optimization problems with uncertainty. Journal of Systems Science and Mathematical Sciences, 2022, 42(5):1190-1199.)
[20] Goberna M A, Jeyakumar V, Li G, et al. Robust solutions of multi-objective linear semi-infinite programs under constraint data uncertainty. SIAM. J. Optim., 2014, 24:1402-1419.
[21] Goberna M A, Jeyakumar V, Li G, et al. Robust solutions to multi-objective linear programs with uncertain data. European J. Oper. Res., 2015, 242:730-743.
[22] Goberna M A, Jeyakumar V, Li G, et al. Radius of robust feasibility formulas for classes of convex programs with uncertain polynomial constraints. Oper. Res. Lett., 2016, 44:67-73.
[23] Chuong T D, Jeyakumar V. An exact formula for radius of robust feasibility of uncertain linear programs. J. Optim. Theory. Appl., 2017, 173:203-226.
[24] Chen J, Li J, Li X, et al. Radius of robust feasibility of system of convex inequalities with uncertain data. J. Optim. Theory. Appl., 2020, 184:384-399.
[25] Goberna M A, Jeyakumar V, Li G. Calculating radius of robust feasibility of uncertain linear conic programs via semi-definite programs. J. Optim. Theory. Appl., 2021, 189:597-622.

基金

国家自然科学基金(12001070),重庆市自然科学基金面上项目(cstc2020jcyjmsxmX0061),重庆市教委科技项目重点项目(KJZD-K202200803)资助课题.
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