Improved twin support vector machine  

作　　者：TIAN YingJie JU XuChan QI ZhiQuan SHI Yong 

机构地区：[1]Research Center on Fictitious Economy and Data Science,Chinese Academy of Sciences [2]School of Mathematical Sciences,University of Chinese Academy of Sciences [3]College of Information Science and Technology,University of Nebraska at Omaha

出　　处：《Science China Mathematics》2014年第2期417-432,共16页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11271361 and 70921061);the CAS/SAFEA International Partnership Program for Creative Research Teams,Major International(Regional)Joint Research Project(Grant No.71110107026);the Ministry of Water Resources Special Funds for Scientific Research on Public Causes(Grant No.201301094);Hong Kong Polytechnic University(Grant No.B-Q10D)

摘　　要：We improve the twin support vector machine(TWSVM)to be a novel nonparallel hyperplanes classifier,termed as ITSVM(improved twin support vector machine),for binary classification.By introducing the diferent Lagrangian functions for the primal problems in the TWSVM,we get an improved dual formulation of TWSVM,then the resulted ITSVM algorithm overcomes the common drawbacks in the TWSVMs and inherits the essence of the standard SVMs.Firstly,ITSVM does not need to compute the large inverse matrices before training which is inevitable for the TWSVMs.Secondly,diferent from the TWSVMs,kernel trick can be applied directly to ITSVM for the nonlinear case,therefore nonlinear ITSVM is superior to nonlinear TWSVM theoretically.Thirdly,ITSVM can be solved efciently by the successive overrelaxation(SOR)technique or sequential minimization optimization(SMO)method,which makes it more suitable for large scale problems.We also prove that the standard SVM is the special case of ITSVM.Experimental results show the efciency of our method in both computation time and classification accuracy.We improve the twin support vector machine（TWSVM）to be a novel nonparallel hyperplanes classifier,termed as ITSVM（improved twin support vector machine）,for binary classification.By introducing the diferent Lagrangian functions for the primal problems in the TWSVM,we get an improved dual formulation of TWSVM,then the resulted ITSVM algorithm overcomes the common drawbacks in the TWSVMs and inherits the essence of the standard SVMs.Firstly,ITSVM does not need to compute the large inverse matrices before training which is inevitable for the TWSVMs.Secondly,diferent from the TWSVMs,kernel trick can be applied directly to ITSVM for the nonlinear case,therefore nonlinear ITSVM is superior to nonlinear TWSVM theoretically.Thirdly,ITSVM can be solved efciently by the successive overrelaxation（SOR）technique or sequential minimization optimization（SMO）method,which makes it more suitable for large scale problems.We also prove that the standard SVM is the special case of ITSVM.Experimental results show the efciency of our method in both computation time and classification accuracy.

关 键 词：support vector machine twin support vector machine nonparallel structural risk minimization CLASSIFICATION 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]