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1、ClusteringMethodsApplicationsofMultivariateStatisticalAnalysisJiangshengYucSchoolofElectronicsEngineeringandComputerSciencePekingUniversity,Beijing,100871yujs@pku.edu.cn,http://icl.pku.edu.cn/yujsClusteringMethods–p.1/48Topics1.What'sclustering?2.SimilarityMeasures3.Hierarch
2、icalClusteringMethods4.NonhierarchicalClusteringMethods5.MultidimentionalScaling6.CorrespondenceAnalysis7.BiplotsforViewingSamplingUnitsandVariables8.ProcrustesAnalysis:AMethod9.Conclusion10.ReferencesClusteringMethods–p.2/48ClusteringProblemExploratoryproceduresarehelpfulin
3、understandingthecomplexnatureofmultivariaterelationships.Problem1Givenasetofdatafx2Rpg,satisfyingi1.thenumberofclassesisunknown;2.theclassofanyindividualisunknown.Weintendto1.de?nesomesuitablestatistics;2.clarifythenumberofclassesK;3.?ndareasonableclusteringmethod;and4.class
4、ifythedataintoKcategories.aaSo,clusteringisalsocalledunsupervisedclassi?cation.ClusteringMethods–p.3/48ExampleofClusteringPartitionagivensetbysomesimilarity:Figure1:fuzzyc-meansclusteringClusteringMethods–p.4/48ObservationMatrixGivennsamplepoints,eachhasmvariables:X1Xj
5、Xmx1x11x1jx1m......xixi1xijxim......xnxn1xnjxnmmeanx1xixmstds1sismTable1:ObservationdataClusteringMethods–p.5/48NoBestClusteringMethod
6、}~?AKQJClusteringMethods–p.6/48ClusterMethods1.SystemMethod:mergethemostsimilarclasses,updatethedataandrepe
7、attheproceduretillalldataareclassi?ed.2.DynamicMethod:giveaninitialclassi?cationofdata?rstly,thenadjusttheclassesbyleastvalueoflossfunctiontillnoimprovementcanmade.3.FuzzyMethod:forinstancefuzzyc-meansclustering,usuallyworkswellfordatawithfuzzycharacteristics.4.MethodofMinim
8、umSpanningTree5.ClusteringMethods–p.7/48TransformationofDataCentralization:makethemean0,andthevariance-covariancematrixunchanged.xij=xij
