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thisway,thefeaturevectorof3Dmodelscontainsmoreinformation.Itusesfine-grainedfeaturestodescribe3Dmodels,soitismoreaccurateanditcanimprovetheretrievalprecision.AffinityPropagationClusteringMethod
Affinitypropagationclustering(AP)isanewclusteringalgorithmanditsrunspeedisfastevenformulti-classificationproblem.BeforetheiterationprocessofAP,thesimilaritymatrix:consistingofthesimilaritybetweendatapointsisfedasinput.Thealgorithmfirsttakesallthedatapointsasthepotentialclustercentersandsupposesthattherearemessagesenergyandbetweenanytwodatapointsiandk.Theisvaluemessagesentfrompointtothecandidateclustercenterpoint,whichisusedtoevaluatewhetherthepointisofsuitabilityastheclustercenterforthepoint,isthevaluemessagesentfromcandidateclustercenterstopoint,whichisusedtoevaluatewhetherthepointisreadytoselectthepointastheclustercenters.Thestrongertheinformationenergyandare,themorepossiblethepointisastheclusteringcenter,whilethepointismorepossibletobelongtotheclasswiththecenterpoint.Theexpressionsofandareshowninthefollowingequations.
(6)
(7)
Inordertoavoidvibrationsduringtheiterationprocess,thedampingfactorisintroducedinthealgorithm,andthemessageenergyintheiterationis:
(8)
(9)
ThediagonalvaluesinSmatrixareusedastheevaluationcriteriaforapointbeingaclustercenter,whichiscalledthebiasparameter.Generally,themedianofallnon-diagonalelementsisadoptedasthevalueof.TheparameterisusedinEq.(10).
(10)
Alargerleadstolargerand,whichmeansthepointismorepossibletobethefinalclustercenter.Whenislarger,morepointstendtobethefinalclustercenters.Therefore,enlargingornotcanincreaseordecreaseclusternumbersproducedbyAP.
ThestepsofAPalgorithmareasfollows:
(1)InitializingtheelementsofsimilaritymatrixS,attractionmatrixRandtheattributionmatrixAas0,andthedampingfactor,thenumberofiterations,themaintainnumberofclusterin
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(2)Thenewattractionandnewattributions,initerationarecalculatedbyEqs.(6)to(7),
(3)Thefinalattractionandfinalattributions,initerationtarecalculatedbyEqs.(8)to(9),
(4)Findingtherepresentativepointsbytheequation,
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(5)Repeatingsteps(2)-(4)untiltherepresentativepointskeepconsistentduringmanytimesiterationor.
AccordingtoAPalgorithm,itassumesthatalltheclustersinfeaturespacearepact.InAP,theenergyfunctionisthesumofsimilaritiesbetweensamplesandclustercenters,whichis.SupposingthatthenumberofclustersisJ,andAPminimizes.Thus,iftheclusterstructureispact,itiseasytoguaranteethateachissmall,andthenissmall,soAPcanachievegoodresultsinthiscondition.Butiftheclusterstructureisloose,thatistosay,theclustersarenotveryclear,APalgorithmtendstoproducemoreclusterstomakeeveryandminimize,soAPwouldproducetoomanyclusters,andtheresultsarenotaccurate.
InordertoimprovetheaccuracyofAPalgorithmandmakethealgorithmeffectivewhenthescaleofmodelsetchangesortheplexdegreeofmodelschanges,thesemi-supervisedAPclusteringalgorithm(S-AP)inRef.[12]isutilizedtocluster3Dmodels.
InS-APalgorithm,theclusteringcentersarealsodeterminedaccordingtosmaller,buttheobjectivefunctionisnotminimizing,whileitusesvalidityindextosupervisetheclustering.TheSilhouetteindex[13]isusedasthevalidityindex.
Supposingthatistheaveragedissimilarityordistancebetweensampletinclusterandalltheothersamplesinthiscluster,whileistheaveragedissimilarityordistancebetweensampletandsamplesinanothercluster,and.ThentheSilhouetteindexofsampletis.
Theaverageofvaluesofallthesamplesindatasetcanrepresentthequalityoftheclusteringresults.ThelargeraverageSilhouetteindexis,thebetterthequalityofclusteringis,sotheclusterresultsofthemaximumindexisthebestresultofclustering.InAP,thenumberofclustersincreasesanddecreaseswiththeincreaseanddecreaseofthevalueofp.InS-AP,theinitialvalueofpisthemedianofattractiondegree,anditsvaluedecreasesdynamicallytoobtainsmallernumberofclusters.Thenthemaximumanditsclusteringresultsareobtained.Theincrementofpis,whereistheminimumofattractiondegree.TheflowofS-APalgorithmisshowninFig.10.
Fig.10FlowofS-AP
APalgorithmisanunsupervisedmethod,butsearchingrepresentativemodelsasclustercentersin3Dmodelsisaclassificationproblemwhichisasupervisedproblem.InordertoenhancetheeffectivenessofAPalgorithm,thesimilaritymatrixSwhichisinputintothealgorithmismodified.
Inthisstudy,thesimilaritybetweentwosamplesinoneclustermultipliesaweighttoincreasetheinformationenergybetweensamplesinoneclusteranddecreasetheinformationenergybetweensamplesindifferentclusters.Thismodificationcanmaketheclustercentermodelmorerepresentativeb
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