非负矩阵分解及在人脸识别的应用PPT格式课件下载.ppt

非负矩阵分解及在人脸识别的应用PPT格式课件下载.ppt

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D.D.LeeandS.Seung,”Learningthepartsofobjectsbynon-negativematrixfactorization”Nature,vol.401,pp.788-791,1999作者的相关信息DanielD.Lee,Ph.D.lAssociateProfessorDept.ofElectricalandSystemsEngineeringDept.ofBioengineering（Secondary）GRASP（GeneralRobotics,Automation,Sensing,Perception）Labl203BMoore/6314UniversityofPennsylvania200S.33rdStreetPhiladelphia,PA19104215-898-8112215-573-2068（FAX）lEmail:

ddleeseas.upenn.edulhttp:

/www.seas.upenn.edu/ddlee/H.SebastianSeunglProfessorofComputationalNeuroscience,MITInvestigator,HowardHughesMedicalInstitutelMIT,46-506543VassarSt.Cambridge,MA02139voice:

617-252-1693seungmit.edulAdministrativeassistant:

AmyDunnvoice:

617-452-2694fax:

617-452-2913adunnmit.edulhttp:

/hebb.mit.edu/people/seung/ProblemStatementGivenasetofimages:

1.Createasetofbasisimagesthatcanbelinearlycombinedtocreatenewimages2.Findthesetofweightstoreproduceeveryinputimagefromthebasisimages3.DimensionreductionlPCAlNMFlLNMFlFNMFlWNMFMainlyDiscussPCAlFindasetoforthogonalbasisimageslThereconstructedimageisalinearcombinationofthebasisimagesWhatdontwelikeaboutPCA?

lPCAinvolvesaddingupsomebasisimagesthensubtractingotherslBasisimagesarentphysicallyintuitivelSubtractingdoesntmakesenseincontextofsomeapplicationslHowdoyousubtractaface?

lWhatdoessubtractionmeaninthecontextofdocumentclassification?

backNon-negativeMatrixFactorizationlLikePCA,exceptthecoefficientsinthelinearcombinationcannotbenegativeNon-negativematrixfactorization（NMF）（Lee&

Seung-2001）NMFgivesPartbasedrepresentation（Lee&

SeungNature1999）NMFisbasedonGradientDescentNMF:

VWHs.t.Wi,d,Hd,j0LetCbeagivencostfunction,thenupdatetheparametersaccordingto:

TheideabehindmultiplicativeupdatesPositivetermNegativetermTheNMFdecompositionisnotuniqueNMFonlyuniquewhendataadequatelyspansthepositiveorthant（Donoho&

Stodden-2004）NMFBasisImagesnmf_basislOnlyallowingaddingofbasisimagesmakesintuitivesenseHasphysicalanalogueinneuronslForcingthereconstructioncoefficientstobepositiveleadstonicebasisimagesToreconstructimages,allyoucandoisaddinmorebasisimagesThisleadstobasisimagesthatrepresentpartsFaceslTrainingset:

2429exampleslFirst25examplesshownatrightlSetconsistsof19x19centeredfaceimagesFaceslBasisImages:

Rank:

49Iterations:

50Facesx=OriginalFacesx=OriginalbackbackExampleLocalnon-negativematrixfactorizationLettingLNMFisaimedatlearninglocalfeaturesbyimposingthefollowingthreeadditionalconstraintsontheNMFbasis:

backbackLNMF_basisLNMF_basisFishernon-negativematrixfactorizationbackbackWeightedNMFbackback结论及未来工作l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。

l问题

（1）非平衡样本集识别率低的问题

（2）权重选取问题参考文献l1D.D.LeeandH.S.Seung,“Learningthepartsofobjectsbynon-negativematrixfactorization”,Nature,vol.401,pp.788-791,1999l2D.D.LeeandH.S.Seung“Algorithmsfornon-negativeMatrixfactorization”，inProceedingsofNeuralInformationProcessingSystems,2000.l3S.Z.Li,X.Hou,H.J.Zhang,andQ.Cheng,“Learningspatiallylocalized,parts-basedrepresentation”,Proc.IEEEInt.Conf.ComputerVisionandPatternRecognition,2001,pp.207-212l4J.LuandY.-P.Tan,“Doublyweightednonnegativematrixfactorizationforimbalancedfacerecognition”,Proc.IEEEInt.Conf.Acoustics,Speech,andSignalProcessing,2009,pp.877C880