Matrix Completion for WeaklyWord文件下载.docx
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trainingimagesareannotatedwithasetofkeywordsdescribingtheircontents,butthevisualconceptsarenotexplicitlysegmentedintheimages.
formulatetheweakly-supervisedimageclassificationasalow-rankmatrixcompletionproblem.
三大优势:
(1)convex相较于multiple-instancelearningmethods.Weproposetwoalternativealgorithmsformatrixcompletion——MC-PosandMC-Simplex,motivatedbythemulti-labelimageclassificationproblemandtheadditivehistogramproperty
specificallytailoredtovisualdata,andprovetheirconvergence.
(2)isrobusttolabelingerrors,backgroundnoiseandpartialocclusions.
(3)beusedforsemanticsegmentation.Caneffectivelycapturingeachclassappearance.
Methods——imageclassificationandlocalizaionproblem
MIL-considerimagesasbagswithmanyinstancesdenotingpossibleregionsofinterest(BOWS)
drawbacks:
(1)castasaNP-hardbinaryquadraticproblem、leadtonon-convexmodels、highlysensibletoinitialization、heavilyrelyonanexplicitenumerationofinstances
(2)lackrobustnesstooutliers
(3)Uncleartobeextendedtousepartialinformation,suchasincompletelabelassignmentsormissingfeaturedescriptions.Forinstance,inFig.1aonetrainingimagehasnolabelforthecategorygrass.
Ourmethod——thehistogramofanentireimageisaweightedsumofthehistograminformationofallofitssubparts(tofactorizethehistogramofanimageasaweightedsumofclasshistograms(asmanyasobjectsarepresent)plusanerrortomodelthebackground.)
Usingthisproperty
webypassthecombinatorialnatureoffindingdesiredregionsineverypositiveimage
imageclassificationcanbeposedasarankminimizationproblem,sinceclasshistogramsaresharedacrossimages,andthenumberofclasshistogramsissmallcomparedtothenumberofimages.
amatrixcompletionframework.
1、ClassificationasaMatrixCompletionProblem
⑴theuseofmatrixcompletionforgeneralclassificationtasks
⑵useforweaklysupervisedmulti-labelimageclassificationandlocalization
BydirectlyestimatingC:
theappearanceofindividualclassescanberecoveredfromamulti-labeldatasetthusprovidethelocalizationforeachconceptintheimages.
2、NuclearNormasaConvexSurrogateoftheRankFunction——tominimize(rankisnon-convexandnon-differentiablefunction)
nuclearnorm——Z的奇异值的和
3、AddingRobustnessintoMatrixCompletion
TheresultingoptimizationproblemfindsthebestlabelassignmentYtstanderror
Matrices
suchthattherankofZisminimized,as
4、FixedPointContinuation(FPC)forMC-Pos/MC-Simplex
enjoythesameconvergencepropertiesoffixedpointcontinuation(FPC)methodsforrankminimizationwithoutconstraints.
Albeitconvex,thenuclearnormmakes(24)and(25)notsmooth.SincenuclearnormproblemsarenaturallycastasSemidefinitePrograms,existinginteriorpointmethodsareinapplicableduetothelargedimensionofZ.
FPC--
总结:
1、keyidea
histogramsoffullimagescontaintheinformationforpartscontainedtherein,soweaklysupervisedlearningcanbeformulatedasalow-rankproblemduetoitsaddivenature,andsolvedusingatransductivematrixcompletionframework
2、twonewconvexmethodsforperformingmulti-labelclassificationofhistogramdata,withprovenconvergenceproperties
3、abletofindclasshistogramrepresentationsandprovidelocalizationintheimages.
4、matrixcompletionallowsforhandlingofmissingdata,labelingerrors,backgroundnoiseandpartialocclusions