·1018· 智能系统学报 第15卷 4结束语 [10]YEUNG D S,WANG Defeng,NG W WY,et al.Struc- tured large margin machines:sensitive to data distribu- 在本文中，提出了一种基于能量的结构化最 tions[J].Machine learning,2007,68(2):171-200. 小二乘李生支持向量机，称为ES-LSTWSVM.。首 [11]LANCKRIET G R G,EL GHAOUI L.BHAT- 先使用聚类算法来获取类中的结构信息，然后为 TACHARYYA C,et al.A robust minimax approach to 每个超平面引入能量因子，将传统TWSVM的不 classification[J].The journal of machine learning re- 等式约束转换为基于能量模型的等式约束。这使 search.2002.3:555-582. 得提出的ES-LSTWSVM不仅有较低的计算复杂 [12]HUANG Kaizhu,YANG Haigin,KING I,et al. 度，而且提高了模型的泛化能力。最后，使用“多 Maxi-min margin machine:learning large margin classi- 对一”策略将ES-LSTWSVM扩展到多类分类问题 fiers locally and globally[J].IEEE transactions on neural 中。实验结果表明，所提出的算法具有良好的分 networks,2008.19(2):260-272. 类性能。 [13]XUE Hui,CHEN Songcan,YANG Qiang.Structural reg- ularized support vector machine:a framework for struc- 参考文献： tural large margin classifier[J].IEEE transactions on neur- al networks.2011,22(4:573-587 [1]CORTES C,VAPNIK V N.Support-vector networks[J]. 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[4]KUMAR M A,GOPAL M.Least squares twin support [16]WARD JR J H.Hierarchical grouping to optimize an ob- jective function[J].Journal of the American statistical as- vector machines for pattern classification[J].Expert sys- s0 ciation,1963,58(301):236-244. tems with applications,2009,36(4):7535-7543. [1刀陶莹，杨锋，刘洋，等.K均值聚类算法的研究与优 [5]TIAN Yingjie,QI Zhiquan,JU Xuchan,et al.Nonparallel support vector machines for pattern classification[J].IEEE 化).计算机技术与发展，2018,28(6)：90-92. transactions on cybernetics,2014,44(7):1067-1079. 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[20]XU Xiao,DING Shifei,SHI Zhongzhi.An improved [8]吴青，齐韶维，孙凯悦，等.最小二乘大间隔孪生支持向 density peaks clustering algorithm with fast finding 量机).北京邮电大学学报，2018,41(6)：34-38. cluster centers[J].Knowledge-based systems,2018,158: WU Qing,QI Shaowei,SUN Kaiyue,et al.Least squares 65-74. large margin twin support vector machine[J].Journal of [21]DING Shifei,DU Mingjing,SUN Tongfeng,et al.An en- Beijing University of Posts and Telecommunications. tropy-based density peaks clustering algorithm for mixed 2018,41(6):34-38 type data employing fuzzy neighborhood[J].Knowledge- [9]RIGOLLET P.Generalization error bounds in semi-super- based systems.2017,133:294-313. vised classification under the cluster assumption[J].The [22]SALVADOR S,CHAN P.Determining the number of journal of machine learning research,2007,8:1369-1392. clusters/segments in hierarchical clustering/segmentation4 结束语 在本文中，提出了一种基于能量的结构化最 小二乘孪生支持向量机，称为 ES-LSTWSVM。首 先使用聚类算法来获取类中的结构信息，然后为 每个超平面引入能量因子，将传统 TWSVM 的不 等式约束转换为基于能量模型的等式约束。这使 得提出的 ES-LSTWSVM 不仅有较低的计算复杂 度，而且提高了模型的泛化能力。最后，使用“多 对一”策略将 ES-LSTWSVM 扩展到多类分类问题 中。实验结果表明，所提出的算法具有良好的分 类性能。 参考文献： CORTES C, VAPNIK V N. 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[21] SALVADOR S, CHAN P. Determining the number of clusters/segments in hierarchical clustering/segmentation [22] ·1018· 智 能 系 统 学 报 第 15 卷