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1、ISSN1673-9418CODENJKYTA8E-mail:fcst@vip.163.comJournalofFrontiersofComputerScienceandTechnologyhttp://www.ceaj.org1673-9418/2010/04(07)-0654-08Tel:+86-10-51616056DOI:10.3778/j.issn.1673-9418.2010.07.009*稀疏低秩双线性判别模型及其应用+蒋琳,谭晓阳,刘俊南京航空航天大学信息科学与技术学院,南京210016
2、*SparseLowRankBilinearDiscriminativeModelanditsApplication+JIANGLin,TANXiaoyang,LIUJunCollegeofComputerScience&Technology,NanjingUniversityofAeronautics&Astronautics,Nanjing210016,China+Correspondingauthor:E-mail:ljiang2008@126.comJIANGLin,TANXiaoyang,LI
3、UJun.Sparselowrankbilineardiscriminativemodelanditsapplication.JournalofFrontiersofComputerScienceandTechnology,2010,4(7):654-661.Abstract:“Highdimensionalityandsmallsizesamples”iswidelyencounteredinmanyrealworldmachinelearningapplications.Lowrankapproxi
4、mationtoparametricmatrixhasrecentlybeenproventobeaneffectivemethodtocontrolthecomplexityofmodels.Mostofthepreviouslowrankmethodsarerequiredtospecifythetargetrankbyhandbeforehand(e.g.,principalcomponentanalysis),however,imposingthesparsityconstraintsonthe
5、parametricmatrixcanavoidthis.Inparticular,underabilineardiscriminativeframework,decomposingtheparametricmatrixandsimultaneouslyconstrainingtheirrankswiththesparsity-inducingregularizationwillperformwell.Theresult-ingproblemcanbeefficientlysolvedwithcoord
6、inatedescent.Thismethodisabletotakethespatialinformationofstructureddataintoaccount,leadingtoimprovedgeneralizationcapability.Thefeasibilityandeffectivenessoftheproposedmethodisdemonstratedonasecuritybiometricapplication.Keywords:sparselowrankapproximati
7、on;bilineardiscriminativeframework;principalcomponentanalysis摘要:“高维度小样本”问题是模式识别应用中的主要障碍之一。跨越这一障碍的有效方法之一是采用参数矩阵的低秩逼近,目的是控制模型复杂度。常用的低秩逼近方法需要预先指定目标矩阵秩的大小(如主*TheNationalNaturalScienceFoundationofChinaunderGrantNo.60773060,60905035(国家自然科学基金);theNaturalScience
8、FoundationofJiangsuProvinceofChinaunderGrandNo.BK200922660(江苏省自然科学基金).Received2010-02,Accepted2010-04.蒋琳等：稀疏低秩双线性判别模型及其应用655成分分析)。提出了一种新的基于稀疏约束的低秩判别模型,此模型通过对目标参数进行矩阵分解,然后分别对子成分施加低秩(稀疏)约束,从而达到低秩逼近的目的。进一步将这一思想嵌入一个双边判别模型,并用坐标
