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1、FuzzyEntropyClusteringDatTranandMichaelWagnerHuman-ComputerCommunicationLab.,SchoolofComputing,UniversityofCanberra,ACT2601,AustraliaEmail:{DatT,MichaelW}@ise.canberra.edu.auAbstract-Thewell-knowngeneralisationofhardC-clusteringcriterionH,isdefinedasthedifferenceofthemeans(HCM)cl
2、usteringisfuzzyC-means(FCM)cluster-HCMcriterionJ1andafunctionEmultipliedbyaweightingwhereaweightexponentoneachfuzzymembershipfactorn>0.ThefunctionEIT,whereTisthenumberisintroducedasthedegreeoffuzziness.AnalternativegeneralisationofHCMclusteringisproposedinthispa-ofdatapointsinX,i
3、sthepartsitionentropyfunction-per.Thisiscalledfuzzyentropy(FE)clusteringwhereathewell-knowncluster-validitycriterion.MinimisationweightfactorofthefuzzyentropyfunctionisintroducedoftheobjectivefunctionH,leadstominimisationofJIasthedegreeoffuzzyentropy.Theweightfactorissimi-lartoth
4、eweightexponentandhasaphysicalinterpreta-andmaximisationofE.Theweightfactorniscalledtion.Thenoiseclusteringapproach,thefuzzycovariancethedegreeoffuzzyentropy.Itissimilartotheweightmatrixandthefuzzymixtureweightarealsoproposed.exponentmandhasaphysicalinterpretation.Asn+0,Moreover,
5、wecanshowGaussianmixtureclusteringisre-FEclusteringapproachesHCMclustering.Asn-+CO,gardedasaspecialcaseofFEclustering.SomeillustrativeexamplesareperformedontheButterflyandIrisdata.wehaveonlyasinglecluster.Especially,ageneralisationofFEclusteringisproposed,itincludesGaussianmixtur
6、eclusteringasitsspecialcasewithn=1.Inotherwords,I.INTRODUCTIONGaussianmixtureclusteringcanberegardedasafuzzyClusteringisthegroupingofsimilarobjects[l].Clus-clusteringmethod.teringinthegivenunlabeleddatasetXistoassigntoThenoiseclusteringapproach,thefuzzycovariancedatapointslabelst
7、hatidentify“naturalsubgroups”inmatrixandthefuzzymixtureweightarealsoproposedX[2].Inotherwords,clusteringknownasunsupervisedinthispaper.SomeillustrativeexamplesareperformedlearninginXisapartitioningofXintoCsubsetsorontheButterflyandIrisdata.Cclusters.Themostimportantrequirementist
8、ofind11.HARDC-MEANSCLUSTERINGasuitableme
