[1]周健航,杨绪兵,张福全,等.马氏度量下局部化广义特征值最接近支持向量机[J].南京师范大学学报(自然科学版),2018,41(04):65.[doi:10.3969/j.issn.1001-4616.2018.04.011]
 Zhou Jianhang,Yang Xubing,Zhang Fuquan,et al.Localized GEPSVM Based on Mahalanobis Metric[J].Journal of Nanjing Normal University(Natural Science Edition),2018,41(04):65.[doi:10.3969/j.issn.1001-4616.2018.04.011]
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马氏度量下局部化广义特征值最接近支持向量机()
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《南京师范大学学报》(自然科学版)[ISSN:1001-4616/CN:32-1239/N]

卷:
第41卷
期数:
2018年04期
页码:
65
栏目:
·数学与计算机科学·
出版日期:
2018-12-31

文章信息/Info

Title:
Localized GEPSVM Based on Mahalanobis Metric
文章编号:
1001-4616(2018)04-0065-07
作者:
周健航1杨绪兵1张福全1业巧林1许等平2
(1.南京林业大学信息科学技术学院,江苏 南京 210037)(2.国家林业局调查规划设计院,北京100714)
Author(s):
Zhou Jianhang1Yang Xubing1Zhang Fuquan1Ye Qiaolin1Xu Dengping2
(1.College of Information Science and Technology,Nanjing Forestry University,Nanjing 210037,China)(2.Survey & Planning Institute of State Forestry Administration,Beijing 100714,China)
关键词:
接近支持向量机广义特征值马氏度量凸壳
Keywords:
proximal support vector machinegeneralized eigenvaluesMahalanobis metricconvex hull
分类号:
TP391
DOI:
10.3969/j.issn.1001-4616.2018.04.011
文献标志码:
A
摘要:
局部化广义特征值最接近支持向量机(Localized GEPSVM,LGEPSVM)是从广义特征值最接近支持向量机(GEPSVM:Proximal Support Vector Machine via Generalized Eigenvalues)衍生而来,其原理是在GEPSVM通过求解广义特征值获得两个彼此不平行的超平面的基础上,分别求解两个超平面的凸壳,修改GEPSVM的分类判据为将测试样本归为距其最近凸壳所属的那一类. 分析和实验表明,LGEPSVM较之GEPSVM具有更高的分类精度. 然而,由于LGEPSVM在训练和分类过程中都涉及凸壳计算问题,因而费时较多. 为了缓解这一问题,本文提出的基于马氏度量的最小椭圆凸壳算法MLGEPSVM(LGEPSVM based on Mahalanobis Metric),即分类时只需要判断样本与对应椭圆凸壳的距离. 较之LGEPSVM和GEPSVM,MLGEPSVM具有如下几个特点:(1)给出了马氏度量下的椭圆凸壳计算方法,(2)分类速度更快,(3)更低的存储空间,每类样本仅需存储椭圆凸壳(可通过中心和协方差表示),而不是所有的凸壳顶点. 在人工和标准数据集上的实验,验证了MLGEPSVM的上述性能.
Abstract:
GEPSVM(Proximal Support Vector Machine via Generalized Eigenvalues)have been played more attention in machine learning and pattern recognition. It adopts data fitting to construct classifier,and further leading to two Generalized Eigenvalue problems. One of its variants is Localized GEPSVM,shortly LGEPSVM. Instead of the closest nonparallel planes of GEPSVM,LGEPSVM classifies an unknown sample to the closest convex hulls on the projection plane. Experimental results show that LGEPSVM able to achieve comparable or even better test correctness than GEPSVM. However,due to training convex hull,LGEPSVM would cost much time in training stage. To speed training LGEPSVM,in this paper,we propose a new version LGEPSVM,termed as MLGEPSVM,based on Mahalanobis metric. Concretely,MLGEPSVM aims to find two ellipsoidal convex hulls,and then classify the samples to the class corresponding to its closest ellipsoid. Compared to LGEPSVM and GEPSVM,advantages of MLGEPSVM lie in three aspects:(1)calculation method of ellipsoid convex hull,(2)faster classification speed,and(3)less storage requirement,only ellipsoid convex hull of each class will be stored(the sample center and covariance matrix). Finally,analysis and experiments on artificial and UCI benchmark datasets will validate our foresaid superiorities.

参考文献/References:

[1] SUYKENS J A K,VANDEWALLE J. Least squares support vector machine classifiers[J]. Neural processing letters,1999,9(3):293-300.
[2]LEE Y J,MANGASARIAN O L. RSVM:Reduced support vector machines[C]//Proceedings of the 2001 SIAM International Conference on Data Mining. Society for Industrial and Applied Mathematics. Chicago:Wellesey-Cambridge Press,2001.
[3]MANGASARIAN O L,WILD E W. Proximal support vector machine classifiers[C]//Proceedings KDD-2001:Knowledge Discovery and Data Mining. San Francisco:ACM Press,2001.
[4]MANGASARIAN O L,WILD E W. Multisurface proximal support vector machine classification via generalized eigenvalues[J]. IEEE transactions on pattern analysis and machine intelligence,2006,28(1):69-74.
[5]KHEMCHANDANI R,CHANDRA S. Twin support vector machines for pattern classification[J]. IEEE transactions on pattern analysis and machine intelligence,2007,29(5):905-910.
[6]YE Q,ZHAO C,ZHANG H,et al. Distance difference and linear programming nonparallel plane classifier[J]. Expert systems with applications,2011,38(8):9425-9433.
[7]SHAO Y H,DENG N Y,CHEN W J. A proximal classifier with consistency[J]. Knowledge-based systems,2013,49(49):171-178.
[8]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.
[9]YE Q,ZHAO C,YE N,et al. Localized twin SVM via convex minimization[J]. Neurocomputing,2011,74(4):580-587.
[10]HUANG H,WEI X,ZHOU Y. Twin support vector machines:a survey[J]. Neurocomputing,2018,300:34-43.
[11]张凯军,梁循.马氏距离多核支持向量机学习模型[J]. 计算机工程,2014,40(6):219-225.
[12]ROTH P M,HIRZER M,K?STINGER M,et al. Mahalanobis distance learning for person re-identification[C]//Person re-identification. London:Springer Press,2014.
[13]BEHERA S K,DOGRA D P,ROY P P. Fast recognition and verification of 3D air signatures using convex hulls[J]. Expert systems with applications,2018,100:106-119.
[14]GARCíA S I D,PAJARES G. On-line crop/weed discrimination through the Mahalanobis distance from images in maize fields[J]. Biosystems engineering,2018,166:28-43.
[15]DE LA HERMOSA GONZáLEZ,R R. Wind farm monitoring using Mahalanobis distance and fuzzy clustering[J]. Renewable energy,2018,123:526-540.
[16]SUO M,ZHU B,ZHANG Y,et al. Fuzzy Bayes risk based on Mahalanobis distance and Gaussian kernel for weight assignment in labeled multiple attribute decision making[J]. Knowledge-based systems,2018,152:26-39.
[17]杨绪兵,王一雄,陈斌. 马氏度量学习中的几个关键问题研究及几何解释[J]. 南京大学学报(自然科学版),2013,49(2):133-141.
[18]BENNETT K P,BREDENSTEINER E J. Duality and geometry in SVM classifiers[C]//Seventeenth International Conference on Machine Learning. Stanford:Morgan Kaufmann Publishers Inc. 2000.
[19]CHAU A L,LI X,YU W. Convex and concave hulls for classification with support vector machine[J]. Neurocomputing,2013,122:198-209.
[20]SHANG J,CHEN M,ZHANG H. Fault detection based on augmented kernel Mahalanobis distance for nonlinear dynamic processes[J]. Computers & chemical engineering,2018,109:311-321.
[21]VERMA N,BRANSON K. Sample complexity of learning mahalanobis distance metrics[J]. Computer science,2015:2584-2592.
[22]MAHALANOBIS P C. On the generalized distance in statistics[J]. National institute of science of India,1936,2:49-55.
[23]DAI H. Theory of matrices[M]. Beijing:Science Press,2001.
[24]BIAN Z Q,ZHANG X G. Pattern recognition[M]. Beijing:Tsinghua Press,2005.
[25]XU H L,LONG G Z,BIE X F,et al. Active learning algorithm of SVM combining tri-training semi-supervised learning and convex-hull vector[J]. Pattern recognition and artificial intelligence,2016,1:39-46.
[26]REN D W,HU Z P. Construction of classifiers of approximative convex hull with reduced dimension[J]. Mathematics in practice and theory,2014(18):166-174.
[27]WANG W B. The research of SVM classifier method based on Gilbert algorithm and scaled convex hulls[D]. Fuzhou:Fuzhou University,2014.
[28]ZHANG X K. Research on high-dimensional data visualization methods and visualization classification techniques(Doctoral dissertation)[M]. Harbin:Harbin Institution of Technology,2013.
[29]CAI G X. Research and application of convex hull support vector machine based on two-phase method[J]. Coal technology,2013,32(5):200-202.
[30]杨铭,赵文雨. 基于内点法的凸壳算法在支持向量中的应用[J]. 信息与电脑(理论版),2013(4):144-145.
[31]YAN J,BI S B,WANG D,et.al. Parallel algorithm for computing convex hulls in multi-processor architecture[J]. Computer science,2013,40(2):16-19.
[32]HU Z P,LU L,FENG C S. Research on classification algorithm based on high-dimensional data description[J]. Journal of Yanshan university,2011,35(4):370-376.
[33]LIU Z B,CHEN Z,LIU J G. A novel geometric nearest point algorithm for constructing SVM classifiers[J]. Acta automatica sinica,2010,36(6):791-797.

备注/Memo

备注/Memo:
收稿日期:2018-08-16.
基金项目:国家自然科学基金(31670554、50375057)、江苏省自然科学基金(BK20161527、BK20171543).
通讯联系人:杨绪兵,副教授,研究方向:模式识别、神经计算. E-mail:xbyang@njfu.edu.cn
更新日期/Last Update: 2018-12-30