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ClusteringOverviewPartitioningMethodsK-MeansSequentialLeaderModelBasedMethodsDensityBasedMethodsHierarchicalMethods2Whatisclusteranalysis?FindinggroupsofobjectsObjectssimilartoeachotherareinthesamegroup.Objectsaredifferentfromthoseinothergroups.UnsupervisedLearningNolabelsDatadriven3ClustersInter-ClusterIntra-Cluster4Clusters5ApplicationsofClusteringMarketingFindinggroupsofcustomerswithsimilarbehaviours.BiologyFindinggroupsofanimalsorplantswithsimilarfeatures.BioinformaticsClusteringmicroarraydata,genesandsequences.EarthquakeStudiesClusteringobservedearthquakeepicenterstoidentifydangerouszones.WWWClusteringweblogdatatodiscovergroupsofsimilaraccesspatterns.SocialNetworksDiscoveringgroupsofindividualswithclosefriendshipsinternally.6Earthquakes7ImageSegmentation8TheBigPicture9RequirementsScalabilityAbilitytodealwithdifferenttypesofattributesAbilitytodiscoverclusterswitharbitraryshapeMinimumrequirementsfordomainknowledgeAbilitytodealwithnoiseandoutliersInsensitivitytoorderofinputrecordsIncorporationofuser-definedconstraintsInterpretabilityandusability10PracticalConsiderationsScalingmatters!11NormalizationorNot?1213EvaluationVS.14Evaluation15SilhouetteAmethodofinterpretationandvalidationofclustersofdata.Asuccinctgraphicalrepresentationofhowwelleachdatapointlieswithinitsclustercomparedtootherclusters.a(i):averagedissimilarityofiwithallotherpointsinthesameclusterb(i):thelowestaveragedissimilarityofitootherclusters16Silhouette17K-Means18K-Means19K-Means20K-MeansDeterminethevalueofK.ChooseKclustercentresrandomly.Eachdatapointisassignedtoitsclosestcentroid.Usethemeanofeachclustertoupdateeachcentroid.Repeatuntilnomorenewassignment.ReturntheKcentroids.ReferenceJ.MacQueen(1967):"SomeMethodsforClassificationandAnalysisofMultivariateObservations",Proceedingsofthe5thBerkeleySymposiumonMathematicalStatisticsandProbability,vol.1,pp.281-297.21CommentsonK-MeansProsSimpleandworkswellforregulardisjointclusters.Convergesrelativelyfast.RelativelyefficientandscalableO(t·k·n)t:iteration;k:numberofcentroids;n:numberofdatapointsConsNeedtospecifythevalueofKinadvance.Difficultanddomainknowledgemayhelp.Mayconvergetolocaloptima.Inpractice,trydifferentinitialcentroids.Maybesensitivetonoisydataandoutliers.Meanofdatapoints…NotsuitableforclustersofNon-convexshapes22TheInfluenceofInitialCentroids23TheInfluenceofInitialCentroids24SequentialLeaderClusteringAveryefficientclusteringalgorithm.NoiterationAsinglepassofthedataNoneedtospecifyKinadvance.Chooseaclusterthresholdvalue.Foreverynewdatapoint:Computethedistancebetweenthenewdatapointandeverycluster'scentre.Iftheminimumdistanceissmallerthanthechosenthreshold,assignthenewdatapointtothecorrespondingclusterandre-computeclustercentre.Otherwise,createanewclusterwiththenewdatapointasitscentre.Clusteringresultsmaybeinfluencedbythesequenceofdatapoints.2526GaussianMixture27ClusteringbyMixtureModels28K-MeansRevisited
modelparameterslatentparameters29ExpectationMaximization30
31EM:GaussianMixture3233DensityBasedMethodsGenerateclustersofarbitraryshapes.Robustagainstnoise.NoKvaluerequiredinadvance.Somewhatsimilartohumanvision.34DBSCANDensity-BasedSpatialClusteringofApplicationswithNoiseDensity:numberofpointswithinaspecifiedradiusCorePoint:pointswithhighdensityBorderPoint:pointswithlowdensitybutintheneighbourhoodofacorepointNoisePoint:neitheracorepointnoraborderpointCorePointNoisePointBorderPoint35DBSCANpqdirectlydensityreachablepqdensityreachableoqpdensityconnected36DBSCANAclusterisdefinedasthemaximalsetofdensityconnectedpoints.StartfromarandomlyselectedunseenpointP.IfPisacorepoint,buildaclusterbygraduallyaddingallpointsthataredensityreachabletothecurrentpointset.Noisepointsarediscarded(unlabelled).37HierarchicalClusteringProduceasetofnestedtree-likeclusters.Canbevisualizedasadendrogram.Clusteringisobtainedbycuttingatdesiredlevel.NoneedtospecifyKinadvance.Maycorrespondtomeaningfultaxonomies.38AgglomerativeMethodsBottom-upMethodAssigneachdatapointtoacluster.Calculatetheproximitymatrix.Mergethepairofclosestclusters.Repeatuntilonlyasingleclusterremains.Howtocalculatethedistancebetweenclusters?SingleLinkMinimumdistancebetweenpointsCompleteLinkMaximumdistancebetweenpoints39Example
BAFIMINARMTOBA0662877255412996FI6620295468268400MI8772950754564138NA2554687540219869RM4122685642190669TO9964001388696690SingleLink40Example
BAFIMI/TONARMBA0662877255412FI6620295468268MI/TO8772950754564NA2554687540219RM4122685642190
BAFIMI/TONA/RMBA0662877255FI6620295268MI/TO8772950564NA/RM255268564041Example
BA/NA/RMFIMI/TOBA/NA/RM0268564FI2680295MI/TO5642950
BA/FI/NA/RMMI/TOBA/FI/NA/RM0295MI/TO295042Minvs.Max3652
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