最小二乘大间隔孪生支持向量机
|
摘要
针对最小二乘孪生支持向量机(LSTWSVM)精度较低和可能存在的"奇异性"问题,提出了一种最小二乘大间隔孪生支持向量机(LSLMTSVM).该算法在最小二乘孪生支持向量机的优化目标函数中引入了间隔分布,提高了算法的泛化性能.在目标函数中加入正则项,实现了结构风险最小化,进一步提高了分类能力.实验结果表明,最小二乘大间隔孪生支持向量机比已有的相关算法性能更优.
In order to overcome low accuracy and possible singularity of least squares twin support vector machine(LSTWSVM),a least squares large margin twin support vector machine(LSLMTSVM) is presented. The proposed algorithm improves generalization performance by introducing margin distribution to the optimization objective function of the LSTWSVM. Additionally,the structural risk minimization principle is implemented by adding the regularization term to the objective function which improves classification ability. Experimental results show that LSLMTSVM has better classification performance than the existing algorithm.
In order to overcome low accuracy and possible singularity of least squares twin support vector machine(LSTWSVM),a least squares large margin twin support vector machine(LSLMTSVM) is presented. The proposed algorithm improves generalization performance by introducing margin distribution to the optimization objective function of the LSTWSVM. Additionally,the structural risk minimization principle is implemented by adding the regularization term to the objective function which improves classification ability. Experimental results show that LSLMTSVM has better classification performance than the existing algorithm.
引文
[1] Cortes C,Vapnik V N. Support-vector networks[J].Machine Learning,1995,20(3):273-297.
[2] Vapnik V N. The nature of statistical learning theory[J].Technometrics,1997,38(4):409.
[3]丁晓剑,赵银亮.双边界支持向量机的理论研究与分析[J].北京邮电大学学报,2010,33(2):20-23.Ding Xiaojian,Zhao Yinliang. Theory and analysis ofdouble margin SVM[J]. Journal of Beijing University ofPosts and Telecommunications,2010,33(2):20-23.
[4]马跃峰,梁循,周小平.一种基于全局代表点的快速最小二乘支持向量机稀疏化算法[J].自动化学报,2017,43(1):132-141.Ma Yuefeng,Liang Xun,Zhou Xiaoping. A fast sparsealgorithm for least squares support vector machine basedon global representative points[J]. Acta Automatica Sini-ca,2017,43(1):132-141.
[5]陈素根,吴小俊.改进的投影孪生支持向量机[J].电子学报,2017,45(2):408-416.Chen Sugen,Wu Xiaojun. Improved projection twin sup-port vector machine[J]. Acta Electronica Sinica,2017,45(2):408-416.
[6]刘春红,韩晶晶,商彦磊,等.基于SVM分类的云集群失败作业主动预测方法[J].北京邮电大学学报,2016,39(5):104-109.Liu Chunhong,Han Jingjing,Shang Yanlei,et al. Pre-dicting job failure in cloud cluster:based on SVM classi-fication[J]. Journal of Beijing University of Posts andTelecommunications,2016,39(5):104-109.
[7] Qi Zhiquan,Tian Yingjie,Shi Yong. Robust twin sup-port vector machine for pattern classification[J]. PatternRecognition,2013,46(1):305-316.
[8] Shao Yuanhai, Deng Naiyang, Yang Zhimin. Leastsquares recursive projection twin support vector machinefor classification[J]. Pattern Recognition,2012,45(6):2299-2307.
[9] Chen Sugen,Wu Xiaojun. A new fuzzy twin support vec-tor machine for pattern classification[J]. InternationalJournal of Machine Learning and Cybernetics,2018,9(9):1553-1564.
[10] Tanveer M,Khan M A,Ho S S. Robust energy-basedleast squares twin support vector machines[J]. AppliedIntelligence,2016,45(1):174-186.
[11] Mangasarian O L,Wild E W. Multisurface proximalsupport vector machine classification via generalizedeigenvalues[J]. IEEE Transactions on Pattern Analysisand Machine Intelligence,2006,28(1):69-74.
[12] Jayadeva,Khemchandani R,Chandra S. Twin supportvector machines for pattern classification[J]. IEEETransactions on Pattern Analysis and Machine Intelli-gence,2007,29(5):905-910.
[13] Kumar M A,Gopal M. Least squares twin support vec-tor machines for pattern classification[J]. Expert Sys-tems with Applications,2009,36(4):7535-7543.
[14] Shao Yuanhai,Zhang Chunhua,Wang Xiaobo,et al.Improvements on twin support vector machines[J].IEEE Transactions on Neural Networks,2011,22(6):962-968.
[15]程昊翔,王坚.一种新的孪生大间隔分布机算法[J].控制与决策,2016,31(5):949-952.Cheng Haoxiang,Wang Jian. A novel twin large margindistribution machine[J]. Control and Decision,2016,31(5):949-952.
[16] Vapnik V N. Statistical learning theory[J]. Encyclope-dia of the sciences of learning,1998,41(4):3185.
[17] Blake C. UCI repository of machine learning databases[EB/OL].[2017-06-25]. http:∥www. ics. uci.edu/~mlearn/MLRepository. html.
[2] Vapnik V N. The nature of statistical learning theory[J].Technometrics,1997,38(4):409.
[3]丁晓剑,赵银亮.双边界支持向量机的理论研究与分析[J].北京邮电大学学报,2010,33(2):20-23.Ding Xiaojian,Zhao Yinliang. Theory and analysis ofdouble margin SVM[J]. Journal of Beijing University ofPosts and Telecommunications,2010,33(2):20-23.
[4]马跃峰,梁循,周小平.一种基于全局代表点的快速最小二乘支持向量机稀疏化算法[J].自动化学报,2017,43(1):132-141.Ma Yuefeng,Liang Xun,Zhou Xiaoping. A fast sparsealgorithm for least squares support vector machine basedon global representative points[J]. Acta Automatica Sini-ca,2017,43(1):132-141.
[5]陈素根,吴小俊.改进的投影孪生支持向量机[J].电子学报,2017,45(2):408-416.Chen Sugen,Wu Xiaojun. Improved projection twin sup-port vector machine[J]. Acta Electronica Sinica,2017,45(2):408-416.
[6]刘春红,韩晶晶,商彦磊,等.基于SVM分类的云集群失败作业主动预测方法[J].北京邮电大学学报,2016,39(5):104-109.Liu Chunhong,Han Jingjing,Shang Yanlei,et al. Pre-dicting job failure in cloud cluster:based on SVM classi-fication[J]. Journal of Beijing University of Posts andTelecommunications,2016,39(5):104-109.
[7] Qi Zhiquan,Tian Yingjie,Shi Yong. Robust twin sup-port vector machine for pattern classification[J]. PatternRecognition,2013,46(1):305-316.
[8] Shao Yuanhai, Deng Naiyang, Yang Zhimin. Leastsquares recursive projection twin support vector machinefor classification[J]. Pattern Recognition,2012,45(6):2299-2307.
[9] Chen Sugen,Wu Xiaojun. A new fuzzy twin support vec-tor machine for pattern classification[J]. InternationalJournal of Machine Learning and Cybernetics,2018,9(9):1553-1564.
[10] Tanveer M,Khan M A,Ho S S. Robust energy-basedleast squares twin support vector machines[J]. AppliedIntelligence,2016,45(1):174-186.
[11] Mangasarian O L,Wild E W. Multisurface proximalsupport vector machine classification via generalizedeigenvalues[J]. IEEE Transactions on Pattern Analysisand Machine Intelligence,2006,28(1):69-74.
[12] Jayadeva,Khemchandani R,Chandra S. Twin supportvector machines for pattern classification[J]. IEEETransactions on Pattern Analysis and Machine Intelli-gence,2007,29(5):905-910.
[13] Kumar M A,Gopal M. Least squares twin support vec-tor machines for pattern classification[J]. Expert Sys-tems with Applications,2009,36(4):7535-7543.
[14] Shao Yuanhai,Zhang Chunhua,Wang Xiaobo,et al.Improvements on twin support vector machines[J].IEEE Transactions on Neural Networks,2011,22(6):962-968.
[15]程昊翔,王坚.一种新的孪生大间隔分布机算法[J].控制与决策,2016,31(5):949-952.Cheng Haoxiang,Wang Jian. A novel twin large margindistribution machine[J]. Control and Decision,2016,31(5):949-952.
[16] Vapnik V N. Statistical learning theory[J]. Encyclope-dia of the sciences of learning,1998,41(4):3185.
[17] Blake C. UCI repository of machine learning databases[EB/OL].[2017-06-25]. http:∥www. ics. uci.edu/~mlearn/MLRepository. html.