第14卷第4期 智能系统学报 Vol.14 No.4 2019年7月 CAAI Transactions on Intelligent Systems Jul.2019 D0:10.11992/tis.201806005 网络出版地址：http:/kns.cnki.net/kcms/detail/23.1538.tp.20190321.0909.002.html 弹性网络核极限学习机的多标记学习算法 王一宾2，裴根生，程玉胜2 (1.安庆师范大学计算机与信息学院，安徽安庆246011,2.安徽省高校智能感知与计算重点实验室，安徽安 庆246011) 摘要：将正则化极限学习机或者核极限学习机理论应用到多标记分类中，一定程度上提高了算法的稳定性。 但目前这些算法关于损失函数添加的正则项都基于L2正则，导致模型缺乏稀疏性表达。同时，弹性网络正则 化既保证模型鲁棒性且兼具模型稀疏化学习，但结合弹性网络的极限学习机如何解决多标记问题鲜有研究。 基于此，本文提出一种对核极限学习机添加弹性网络正则化的多标记学习算法。首先，对多标记数据特征空间 使用径向基核函数映射：随后，对核极限学习机损失函数施加弹性网络正则项：最后，采用坐标下降法迭代求 解输出权值以得到最终预测标记。通过对比试验和统计分析表明，提出的算法具有更好的性能表现。 关键词：多标记学习：核极限学习机：正则化：弹性网络：径向基函数：坐标下降法 中图分类号：TP391文献标志码：A 文章编号：1673-4785(2019)04-0831-12 中文引用格式：王一宾，裴根生，程玉胜.弹性网络核极限学习机的多标记学习算法J.智能系统学报，2019,14(4)： 831-842. 英文引用格式：WANG Yibin,PEI Gensheng,.CHENG Yusheng.Multi---label learning algorithm of an elastic net kernel extreme learning machine[J.CAAI transactions on intelligent systems,2019,14(4):831-842. Multi-label learning algorithm of an elastic net kernel extreme learning machine WANG Yibin2,PEI Gensheng',CHENG Yusheng'2 (1.School of Computer and Information,Anqing Normal University,Anqing 246011,China;2.The University Key Laboratory of In- telligent Perception and Computing of Anhui Province,Anqing 246011,China) Abstract:Regularized extreme learning machine or kernel extreme learning machine theory was applied to multi-label classification,which improves the stability of the algorithm to a certain extent.However,the regularization terms added by these algorithms for loss functions are all based on L2 regularization,which leads to the lack of sparse expression of the model.Simultaneously,elastic net regularization guarantees both model robustness and model sparse learning.Nev- ertheless,there is insufficient research on how to solve multi-label learning problems by combining elastic net kernel ex- treme learning machines.Based on this hypothesis,this paper proposes a multi-label learning algorithm that adds elastic network regularization to kernel extreme learning machines.It first uses radial basis function mapping for feature spa- cing of multi-label;subsequently,it applies the elastic net regularization to the loss function of kernel extreme learning machine.Finally,it uses the coordinate descent method to iteratively solve the output weights to get the final prediction labels.Through comparative experiments and statistical analyses,the proposed method demonstrates better performance Keywords:multi-label learning;kernel extreme learning machine;regularization;elastic net;radial basis function;co- ordinate descent 收稿日期：2018-06-02.网络出版日期：2019-03-22 近年来，随着人工智能的迅速发展，标记学习 基金项目：安徽省高校重点科研项目(KJ2017A352):安微省高 校重点实验室基金项目(ACAIM160102). 成为其重点的研究领域之一。其中单标记学习将 通信作者：程玉胜.E-mail:chengyshaq@163.com. 每个示例由一个特征向量和一个标记来描述；而DOI: 10.11992/tis.201806005 网络出版地址: http://kns.cnki.net/kcms/detail/23.1538.tp.20190321.0909.002.html 弹性网络核极限学习机的多标记学习算法 王一宾1,2，裴根生1 ，程玉胜1,2 （1. 安庆师范大学 计算机与信息学院，安徽 安庆 246011; 2. 安徽省高校智能感知与计算重点实验室，安徽 安 庆 246011） 摘 要：将正则化极限学习机或者核极限学习机理论应用到多标记分类中，一定程度上提高了算法的稳定性。 但目前这些算法关于损失函数添加的正则项都基于 L2 正则，导致模型缺乏稀疏性表达。同时，弹性网络正则 化既保证模型鲁棒性且兼具模型稀疏化学习，但结合弹性网络的极限学习机如何解决多标记问题鲜有研究。 基于此，本文提出一种对核极限学习机添加弹性网络正则化的多标记学习算法。首先，对多标记数据特征空间 使用径向基核函数映射；随后，对核极限学习机损失函数施加弹性网络正则项；最后，采用坐标下降法迭代求 解输出权值以得到最终预测标记。通过对比试验和统计分析表明，提出的算法具有更好的性能表现。 关键词：多标记学习；核极限学习机；正则化；弹性网络；径向基函数；坐标下降法 中图分类号：TP391 文献标志码：A 文章编号：1673−4785(2019)04−0831−12 中文引用格式：王一宾, 裴根生, 程玉胜. 弹性网络核极限学习机的多标记学习算法 [J]. 智能系统学报, 2019, 14(4): 831–842. 英文引用格式：WANG Yibin, PEI Gensheng, CHENG Yusheng. Multi-label learning algorithm of an elastic net kernel extreme learning machine[J]. CAAI transactions on intelligent systems, 2019, 14(4): 831–842. Multi-label learning algorithm of an elastic net kernel extreme learning machine WANG Yibin1,2 ，PEI Gensheng1 ，CHENG Yusheng1,2 (1. School of Computer and Information, Anqing Normal University, Anqing 246011, China; 2. The University Key Laboratory of In￾telligent Perception and Computing of Anhui Province, Anqing 246011, China) Abstract: Regularized extreme learning machine or kernel extreme learning machine theory was applied to multi-label classification, which improves the stability of the algorithm to a certain extent. However, the regularization terms added by these algorithms for loss functions are all based on L2 regularization, which leads to the lack of sparse expression of the model. Simultaneously, elastic net regularization guarantees both model robustness and model sparse learning. Nev￾ertheless, there is insufficient research on how to solve multi-label learning problems by combining elastic net kernel ex￾treme learning machines. Based on this hypothesis, this paper proposes a multi-label learning algorithm that adds elastic network regularization to kernel extreme learning machines. It first uses radial basis function mapping for feature spa￾cing of multi-label; subsequently, it applies the elastic net regularization to the loss function of kernel extreme learning machine. Finally, it uses the coordinate descent method to iteratively solve the output weights to get the final prediction labels. Through comparative experiments and statistical analyses, the proposed method demonstrates better performance. Keywords: multi-label learning; kernel extreme learning machine; regularization; elastic net; radial basis function; co￾ordinate descent 近年来，随着人工智能的迅速发展，标记学习 成为其重点的研究领域之一。其中单标记学习将 每个示例由一个特征向量和一个标记来描述；而 收稿日期：2018−06−02. 网络出版日期：2019−03−22. 基金项目：安徽省高校重点科研项目 (KJ2017A352)；安徽省高 校重点实验室基金项目 (ACAIM160102). 通信作者：程玉胜. E-mail：chengyshaq@163.com. 第 14 卷第 4 期 智 能 系 统 学 报 Vol.14 No.4 2019 年 7 月 CAAI Transactions on Intelligent Systems Jul. 2019