非负矩阵分解及在人脸识别的应用PPT课件

.,1,Non-NegativeMatrixFactorization（NMF）,Reportor:MaPeng,Paper:D.D.LeeandS.Seung,”Learningthepartsofobjectsbynon-negativematrixfactorization”Nature,vol.401,pp.788-791,1999,.,2,作者的相关信息,DanielD.Lee,Ph.D.AssociateProfessorDept.ofElectricalandSystemsEngineeringDept.ofBioengineering(Secondary)GRASP(GeneralRobotics,Automation,Sensing,Perception)Lab203BMoore/6314UniversityofPennsylvania200S.33rdStreetPhiladelphia,PA19104215-898-8112215-573-2068(FAX)Email:/ddlee/,.,3,H.SebastianSeungProfessorofComputationalNeuroscience,MITInvestigator,HowardHughesMedicalInstituteMIT,46-506543VassarSt.Cambridge,MA02139voice:617-252-1693Administrativeassistant:AmyDunnvoice:617-452-2694fax:617-452-2913/people/seung/,.,4,ProblemStatement,Givenasetofimages:CreateasetofbasisimagesthatcanbelinearlycombinedtocreatenewimagesFindthesetofweightstoreproduceeveryinputimagefromthebasisimagesDimensionreduction,.,5,PCANMFLNMFFNMFWNMF,MainlyDiscuss,.,6,PCA,FindasetoforthogonalbasisimagesThereconstructedimageisalinearcombinationofthebasisimages,.,7,WhatdontwelikeaboutPCA?,PCAinvolvesaddingupsomebasisimagesthensubtractingothersBasisimagesarentphysicallyintuitiveSubtractingdoesntmakesenseincontextofsomeapplicationsHowdoyousubtractaface?Whatdoessubtractionmeaninthecontextofdocumentclassification?back,.,8,Non-negativeMatrixFactorization,LikePCA,exceptthecoefficientsinthelinearcombinationcannotbenegative,.,9,Non-negativematrixfactorization(NMF),(Lee&Seung-2001),NMFgivesPartbasedrepresentation,(Lee&SeungNature1999),.,10,NMFisbasedonGradientDescent,NMF:VWHs.t.Wi,d,Hd,j0LetCbeagivencostfunction,thenupdatetheparametersaccordingto:,.,11,Theideabehindmultiplicativeupdates,Positiveterm,Negativeterm,.,12,TheNMFdecompositionisnotunique,NMFonlyuniquewhendataadequatelyspansthepositiveorthant(Donoho&Stodden-2004),.,13,NMFBasisImagesnmf_basis,OnlyallowingaddingofbasisimagesmakesintuitivesenseHasphysicalanalogueinneuronsForcingthereconstructioncoefficientstobepositiveleadstonicebasisimagesToreconstructimages,allyoucandoisaddinmorebasisimagesThisleadstobasisimagesthatrepresentparts,.,14,.,15,Faces,Trainingset:2429examplesFirst25examplesshownatrightSetconsistsof19x19centeredfaceimages,.,16,Faces,BasisImages:Rank:49Iterations:50,.,17,Faces,x,=,Original,.,18,Faces,x,=,Original,back,.,19,Example,.,20,Localnon-negativematrixfactorization,.,21,LettingLNMFisaimedatlearninglocalfeaturesbyimposingthefollowingthreeadditionalconstraintsontheNMFbasis:,.,22,.,23,back,LNMF_basis,.,24,Fishernon-negativematrixfactorization,.,25,back,.,26,WeightedNMF,.,27,.,28,back,.,29,结论及未来工作,综上所述，非负矩阵分解是一种的提取图像局部特征信息的有效的方法，目前在很多领域得到广泛应用，值得我们关注。问题（1）非平衡样本集识别率低的问题（2）权重选取问题,.,30,参考文献,1D.D.LeeandH.S.Seung,“Learningthepartsofobjectsbynon-negativematrixfactorization”,Nature,vol.401,pp.788-791,19992D.D.LeeandH.S.Seung“Algorithmsfornon-negativeMatrixfactorization”，inProceedingsofNeuralInformationProcessingSystems,2000.3S.Z.Li,X.Hou,H.J.Zhang,andQ.Cheng,“Learningspatiallylocalized,parts-basedrepresentation”,Proc.IEEEInt.Conf.ComputerVisionandPatternRecognition,2001,pp.207-212