非负矩阵分解及在人脸识别的应用.ppt
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Non-NegativeMatrixFactorization(NMF)Reportor:
MaPengPaper:
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