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ClusteringClusteringOverviewPartitioningMethodsK-MeansSequentialLeaderModelBasedMethodsDensityBasedMethodsHierarchicalMethods2OverviewPartitioningMethods2Whatisclusteranalysis?FindinggroupsofobjectsObjectssimilartoeachotherareinthesamegroup.Objectsaredifferentfromthoseinothergroups.UnsupervisedLearningNolabelsDatadriven3Whatisclusteranalysis?FindiClustersInter-ClusterIntra-Cluster4ClustersInter-ClusterIntra-CluClusters5Clusters5ApplicationsofClusteringMarketingFindinggroupsofcustomerswithsimilarbehaviours.BiologyFindinggroupsofanimalsorplantswithsimilarfeatures.BioinformaticsClusteringmicroarraydata,genesandsequences.EarthquakeStudiesClusteringobservedearthquakeepicenterstoidentifydangerouszones.WWWClusteringweblogdatatodiscovergroupsofsimilaraccesspatterns.SocialNetworksDiscoveringgroupsofindividualswithclosefriendshipsinternally.6ApplicationsofClusteringMarkEarthquakes7Earthquakes7ImageSegmentation8ImageSegmentation8TheBigPicture9TheBigPicture9RequirementsScalabilityAbilitytodealwithdifferenttypesofattributesAbilitytodiscoverclusterswitharbitraryshapeMinimumrequirementsfordomainknowledgeAbilitytodealwithnoiseandoutliersInsensitivitytoorderofinputrecordsIncorporationofuser-definedconstraintsInterpretabilityandusability10RequirementsScalability10PracticalConsiderationsScalingmatters!11PracticalConsiderationsScalinNormalizationorNot?12NormalizationorNot?121313EvaluationVS.14EvaluationVS.14Evaluation15Evaluation15SilhouetteAmethodofinterpretationandvalidationofclustersofdata.Asuccinctgraphicalrepresentationofhowwelleachdatapointlieswithinitsclustercomparedtootherclusters.a(i):averagedissimilarityofiwithallotherpointsinthesameclusterb(i):thelowestaveragedissimilarityofitootherclusters16SilhouetteAmethodofinterpreSilhouette17Silhouette17K-Means18K-Means18K-Means19K-Means19K-Means20K-Means20K-MeansDeterminethevalueofK.ChooseKclustercentresrandomly.Eachdatapointisassignedtoitsclosestcentroid.Usethemeanofeachclustertoupdateeachcentroid.Repeatuntilnomorenewassignment.ReturntheKcentroids.ReferenceJ.MacQueen(1967):"SomeMethodsforClassificationandAnalysisofMultivariateObservations",Proceedingsofthe5thBerkeleySymposiumonMathematicalStatisticsandProbability,vol.1,pp.281-297.21K-MeansDeterminethevalueofCommentsonK-MeansProsSimpleandworkswellforregulardisjointclusters.Convergesrelativelyfast.RelativelyefficientandscalableO(t?k?n)t:iteration;k:numberofcentroids;n:numberofdatapointsConsNeedtospecifythevalueofKinadvance.Difficultanddomainknowledgemayhelp.Mayconvergetolocaloptima.Inpractice,trydifferentinitialcentroids.Maybesensitivetonoisydataandoutliers.Meanofdatapoints…NotsuitableforclustersofNon-convexshapes22CommentsonK-MeansPros22TheInfluenceofInitialCentroids23TheInfluenceofInitialCentrTheInfluenceofInitialCentroids24TheInfluenceofInitialCentrSequentialLeaderClusteringAveryefficientclusteringalgorithm.NoiterationAsinglepassofthedataNoneedtospecifyKinadvance.Chooseaclusterthresholdvalue.Foreverynewdatapoint:Computethedistancebetweenthenewdatapointandeverycluster'scentre.Iftheminimumdistanceissmallerthanthechosenthreshold,assignthenewdatapointtothecorrespondingclusterandre-computeclustercentre.Otherwise,createanewclusterwiththenewdatapointasitscentre.Clusteringresultsmaybeinfluencedbythesequenceofdatapoints.25SequentialLeaderClusteringA2626GaussianMixture27GaussianMixture27ClusteringbyMixtureModels28ClusteringbyMixtureModels28K-MeansRevisited

modelparameterslatentparameters29K-MeansRevisited

modelparamExpectationMaximization30ExpectationMaximization30

31

31EM:GaussianMixture32EM:GaussianMixture323333DensityBasedMethodsGenerateclustersofarbitraryshapes.Robustagainstnoise.NoKvaluerequiredinadvance.Somewhatsimilartohumanvision.34DensityBasedMethodsGenerateDBSCANDensity-BasedSpatialClusteringofApplicationswithNoiseDensity:numberofpointswithinaspecifiedradiusCorePoint:pointswithhighdensityBorderPoint:pointswithlowdensitybutintheneighbourhoodofacorepointNoisePoint:neitheracorepointnoraborderpointCorePointNoisePointBorderPoint35DBSCANDensity-BasedSpatialClDBSCANpqdirectlydensityreachablepqdensityreachableoqpdensityconnected36DBSCANpqdirectlydensityreachDBSCANAclusterisdefinedasthemaximalsetofdensityconnectedpoints.StartfromarandomlyselectedunseenpointP.IfPisacorepoint,buildaclusterbygraduallyaddingallpointsthataredensityreachabletothecurrentpointset.Noisepointsarediscarded(unlabelled).37DBSCANAclusterisdefinedasHierarchicalClusteringProduceasetofnestedtree-likeclusters.Canbevisualizedasadendrogram.Clusteringisobtainedbycuttingatdesiredlevel.NoneedtospecifyKinadvance.Maycorrespondtomeaningfultaxonomies.38HierarchicalClusteringProduceAgglomerativeMethodsBottom-upMethodAssigneachdatapointtoacluster.Calculatetheproximitymatrix.Mergethepairofclosestclusters.Repeatuntilonlyasingleclusterremains.Howtocalculatethedistancebetweenclusters?SingleLinkMinimumdistancebetweenpointsCompleteLinkMaximumdistancebetweenpoints39AgglomerativeMethodsBottom-upExample

BAFIMINARMTOBA0662877255412996FI6620295468268400MI8772950754564138NA2554687540219869RM4122685642190669TO9964001388696690SingleLink40Example

BAFIMINARMTOBA06628772Example

BAFIMI/TONARMBA0662877255412FI6620295468268MI/TO8772950754564NA2554687540219RM412268564219

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