v〓 -支持向量机克服了传统支持向量机选取参数的困难问题,然而,该方法并未考虑不同样本在训练中的作用,从而导致该方法对噪声或孤立点具有较强的敏感性,使得训练易出现过拟合现象.为了解决这些问题,针对不同样本的作用,通过引入样本的权重,获得了一种改进的v〓 -支持向量机模型,使用Lagrange方法对该模型求解,获得了一种支持向量机分类器.实验中选取来自于UCI数据库的10个标准数据集,针对2种不同的确定样本权重的方法,验证了提出方法的有效性,并与C-SVM和v〓 -SVM进行了性能比较.
The v-support vector machine(v-SVM)overcomes the difficult problem with selection of parameter for the traditional support vector machine.However,this method does not take into account the effect of different samples in the process of training,which leads to a strong sensitivity to noise or outlier points so that training is easy to be over-fit.In order to solve this problem,an improved v-SVM model is obtained by introducing the weight of the samples for the effect of different samples.A Lagrange method is used to solve the model,and a support vector machine classifier is obtained.To show the effectiveness of the presented method,the experiments are conducted using at two kinds of methods for determining weights of samples on 10 standard data sets from UCI repository,and compared with the performance of C-SVM and v-SVM.
[1] VAPNIK V N.The nature of statistical learning theory [M].New York: Springer,1995.
[2] SCHOLKOPF B,SMOLA A J,WILLIAMSON R C,et al.New support vector algorithms [J].Neural Computation,2000,12(5): 1207-1245.DOI: 10.1162/089976600300015565.
[3] BLOOM V,GRIVA L,KWON B,et al.Exterior-point method for support vector machines[J].IEEE Transactions on Neural Networks and Learning Systems,2014,25(7): 1390-1393.
[4] LIN C F,WANG S D.Fuzzy support vector machines [J].IEEE Transaction on Neural Networks,2002,13(2): 464-471.DOI: 10.1109/72.991432.
[5] YANG X W,ZHANG G Q,LU J.A kernel fuzzy c-means clustering-based fuzzy support vector machine algorithm for classification problems with outliers or noises [J].IEEE Transactions on Fuzzy Systems,2011,19(1): 105-115.
[6] XU Y T.A rough margin-based linear υ support vector regression [J].Statistics and Probability Letters,2012,82(3):528-534.
[7] CHEN D G,HE Q,WANG X Z. FRSVMs: Fuzzy rough set based support vector machines [J].Fuzzy Sets and Systems,2010,161: 596-607.
[8] PLATT J.Fast training of support vector machines using sequential minimal optimization[C] //SCHÖLKOPF B,BURGES C J C,SMOLA A J(Eds.).Advances in Kernel Methods—Support Vector Learning.MIT Press,Cambridge,MA,1999:185-208.
[9] JOACHIMS T.Making large-scale SVM learning practical[C] //SCHÖLKOPF B,BURGES C J C,SMOLA A J(Eds.).Advances in Kernel Methods: Support Vector Machine.MIT Press,Cambridge,MA,1999,169-184.
[10] YEUNG D,WANG D,NG W,et al.Structured large margin machines: sensitive to data distributions [J].Machine Learning,2007,68(2):171-200.
[11] XUE H,CHEN S C,YANG Q.Structural regularized support vector machine: a framework for structural large margin classifier[J].IEEE Transactions on Neural Networks,2011,22(4):573-587.
[12] ZHANG L,ZHOU W D.Fisher-regularized support vector machine[J].Information Sciences,2016,343-344:79-93.
[13] CHAPELLE O.Training a Support Vector Machine in the Primal[J].Neural Computation,2007,19(5):1155-1178.
[14] SUYKENS J,VANDEWALLE J.Least squares support vector machine classifiers [J].Neural Processing Letters,1999,9(3): 293-300.DOI: 10.1023/ A: 1018628609742.
[15] BLAKE C,MERZ C J.UCI Repository for machine learning databases[EB/OL].(1998-01-12)[2014-09-06].IrvineCA:University of California,Department of Information and Computer Sciences.http://www.ics.uci.edu/mlearn/MLRep.