计算机科学 ›› 2018, Vol. 45 ›› Issue (4): 100-105.doi: 10.11896/j.issn.1002-137X.2018.04.015

• 2017年全国理论计算机科学学术年会 • 上一篇    下一篇

基于L1-范数距离的最小二乘对支持向量机

周燕萍,业巧林   

  1. 无锡科技职业学院物联网与软件技术学院 江苏 无锡214028,南京林业大学信息科学与技术学院 南京210037
  • 出版日期:2018-04-15 发布日期:2018-05-11
  • 基金资助:
    本文受江苏省自然科学基金(BK20171453)资助

L1-norm Distance Based Least Squares Twin Support Vector Machine

ZHOU Yan-ping and YE Qiao-lin   

  • Online:2018-04-15 Published:2018-05-11

摘要: 最小二乘对支持向量机(LSTSVM)是一种有效的分类技术。然而,该方法需计算点到平面的平方L2-范数距离,从而易受野值或噪声的影响。为了缓解此问题,提出了一种有效的鲁棒 LSTSVM方法,即基于L1-范数距离的LSTSVM(LSTSVML1D)。该方法由于使 用L1范数作为距离度量,因此不易受到野值或噪声数据的影响。此外,设计了一种有效的迭代算法,旨在求解目标问题,并从理论上证明了其收敛性。在人工数据集和UCI数据集上验证了LSTSVML1D 的有效性。

关键词: 最小二乘支持向量机,基于L1-范数距离的LSTSVM,L1范数距离,L2范数平方距离

Abstract: Recently,LSTSVM,as an efficient classification algorithm,was proposed.However,this algorithm computes squared L2-norm distances from planes to points,such that it is easily affected by outliers or noisy data.In order to avoid this problem,this paper presented an efficient L1-norm distance based robust LSTSVM method,termed as LSTSVML1D.LSTSVML1D computes L1-norm distances from planes to points and is not sensitive to outliers and noise.Besides,this paper designed an efficient iterative algorithm to solve the resulted objective,and proved its convergence.Experiments on artificial dataset and UCI dataset indicate the effectiveness of the proposed LSTSVML1D.

Key words: Least squares support vector machine,L1-norm distance based LSTSVM,L1-norm distance,Squared L2-norm distance

[1] SMITH R S,KITTLER J,HAMOUZ M,et al.Face RecognitionUsing Angular LDA and SVM Ensembles[C]∥18th International Conference on Pattern Recognition(ICPR 2006).2006:1008-1012.
[2] C J,LIN C W,HSU,et al.A practical guide to support vector classification.http://www.csie.ntu.edu.tw/ cjlin/papers/guide/guide.pdf.
[3] IVOR W T,JAMES T K,CHEUNG P K.Fast SVM Training on Very Large Data Sets[J].Journal of Machine Learning Research,2005(6):363-392.
[4] FRANC V,SONNENBURG S.Optimized cutting plane algo-rithm for large-scale risk minimization[J].Journal of Machine Learning Research,2009(10):2157-2192.
[5] MANGASARIAN O,WILD E.Multisurface proximal supportvector machine classification via generalized eigenvalues[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2006,28(1),69-74.
[6] JAYADEVA,KHEMCHANDANI R,CHANDRA S.Fuzzy mul-ti-category proximal support vector classification via generalized eigenvalues[J].Soft Comput,2007,1:679-685.
[7] GUARRACINO M R,CIFARELLI C,SEREF O,et al.A Parallel Classification Method for Genomic and Proteomic Problems[C]∥20th International Conference on Advanced Information Networking and Applications(AINA’06).2006:588-592.
[8] YANG X B,CHEN S C.Proximal Support Vector MachineBased on Prototypal Multiclassfication Hyperplanes[J].Journal of Computer Research and Development,2006,3(10):1700-1705.(in Chinese) 杨绪兵,陈松灿.基于原型超平面的多类最接近支持向量机[J].计算机研究与发展,2006,43(10):1700-1705.
[9] YANG X B,CHEN S C,YANG Y M.Localized proximal support vector machine via generalized eigenvalues[J].Chinese Journal of Computers,2007,0(8):1227-1234.(in Chinese) 杨绪兵,陈松灿,杨益民.局部化的广义特征值最接近支持向量机[J].计算机学报,2007,30(8):1227-1234.
[10] YE Q L,ZHAO C X,YE N,et al.Multi-Weight Vector Projection Support vector machines[J].Pattern Recognition Letters,2010,31:2006-2011.
[11] YE Q L,YE N,YIN T M.Enhanced multi-weight vector projection support vector machine[J].Pattern Recognition Letters,2014,42:91-100.
[12] JAYADEVA,KHEMCHANDAI R,CHANDRA S.Twin sup-port vector machines for pattern classification[J].IEEE Transaction on Pattern Analysis and Machine Intelligence,2007,29(5):905-910.
[13] TIAN Y,QI Z,JU X,et al.Nonparallel support vector machines for pattern classification[J].IEEE Transactions on Cybernetics,2014,44(7):1067.
[14] CEVIKALP H.Best Fitting Hyperplanes for Classification[J].IEEE Transactions on Pattern Analysis & Machine, 2017,39(6):1076-1088.
[15] QI Z,TIAN Y,SHI Y.Structural twin support vector machine for classification[J].Knowledge-Based Syst.,2013,43:74-81.
[16] SHAO Y H,CHEN W J,WANG Z,et al.Weighted linear loss twin support vector machine for large-scale classification[J].Knowledge-Based Systems,2014,73(1):276-288.
[17] KHEMCHANDANI R,SAIGAL P,CHANDRA S.Improve-ments on ν-Twin Support Vector Machine[J].Neural Netw.,2016,7(79):97-107.
[18] KUMAR M A,GOPA M.Application of smoothing techniqueon twin support vector machines[J].Pattern Recognition Letters,2008,29:1842-1848.
[19] YE Q L,ZHAO C X.A Feature Selection Method for TWSVM via a Regularization Technique[J].Journal of Computer Research and Development,2011,8(6):1029-1037.(in Chinese) 业巧林,赵春霞.基于正则化的TWSVM 特征选择算法[J].计算机研究与发展,2011,48(6):1029-1037.
[20] KUMAR M A,GOPAL M.Least squares twin support vector machines for pattern classification[J].Expert Systems with Applications,2009,36(4):7535-7543.
[21] WANG H X,LU X S,HU Z L,et al.Fisher discriminant analysis with L1-norm[J].IEEE Trans.Cybern.,2014,6(44):828-842.
[22] LI C N,SHAO Y H,DENG N Y.Robust L1-norm non-parallel proximal support vector machine[J].Optimization,2016,65(1):1-15.
[23] ZHENG W M,LIN Z C,WANG H X.L1-norm distance Kernel Discriminant Analysis via Bayes Error Bound Optimization for Robust Feature Extraction[J].IEEE Trans.Neural Netw.,2014,4(24):793-805.
[24] WANG H,TANG Q,ZHENG W M.L1-Norm-Based Common Spatial Patterns[J].IEEE Trans.Biomed.Engineering,2012,59(3):653-662.

No related articles found!
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!