Matrix Completion for Weakly.docx

Matrix Completion for Weakly.docx

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MatrixCompletionforWeakly

MatrixCompletionforWeakly-SupervisedMulti-LabelImageClassification

Abstract—

aweakly-supervisedsystemformulti-labelimageclassification.

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