基于多元统计分析的聚类方法

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1、ClusteringMethodsApplicationsofMultivariateStatisticalAnalysisJiangshengYucSchoolofElectronicsEngineeringandComputerSciencePekingUniversity,Beijing,100871yujs@pku.edu.cn,http://icl.pku.edu.cn/yujsClusteringMethods–p.1/48Topics1.What'sclustering?2.SimilarityMeasures3.HierarchicalClusteringMetho

2、ds4.NonhierarchicalClusteringMethods5.MultidimentionalScaling6.CorrespondenceAnalysis7.BiplotsforViewingSamplingUnitsandVariables8.ProcrustesAnalysis:AMethod9.Conclusion10.ReferencesClusteringMethods–p.2/48ClusteringProblemExploratoryproceduresarehelpfulinunderstandingthecomplexnatureofmultiva

3、riaterelationships.Problem1Givenasetofdatafx2Rpg,satisfyingi1.thenumberofclassesisunknown;2.theclassofanyindividualisunknown.Weintendto1.definesomesuitablestatistics;2.clarifythenumberofclassesK;3.findareasonableclusteringmethod;and4.classifythedataintoKcategories.aaSo,clusteringisalsocalledunsu

4、pervisedclassi®cation.ClusteringMethods–p.3/48ExampleofClusteringPartitionagivensetbysomesimilarity:Figure1:fuzzyc-meansclusteringClusteringMethods–p.4/48ObservationMatrixGivennsamplepoints,eachhasmvariables:X1


Xj


Xmx1x11


x1j


x1m......xixi1


xij


xim......xnxn1


xnj


xnmmeanx1


x

5、i


xmstds1


si


smTable1:ObservationdataClusteringMethods–p.5/48NoBestClusteringMethod

6、}~•AKQJClusteringMethods–p.6/48ClusterMethods1.SystemMethod:mergethemostsimilarclasses,updatethedataandrepeattheproceduretillalldataareclassified.2.DynamicMethod:giveaninitialclassificationofdatafirstly,th

7、enadjusttheclassesbyleastvalueoflossfunctiontillnoimprovementcanmade.3.FuzzyMethod:forinstancefuzzyc-meansclustering,usuallyworkswellfordatawithfuzzycharacteristics.4.MethodofMinimumSpanningTree5.


ClusteringMethods–p.7/48TransformationofDataCentralization:makethemean0,andthevariance-covarian

8、cematrixunchanged.xij=xijxj(1)S=S=(sij)mm(2)1Xn1Xnsij=(xtixi)(xtjxj)=xtixtj(3)n1n1t=1t=1Standardization:makethemean0,andsdt1.xijxjx=(4)ijsjClusteringMethods–p.8/48MeasuringSimilarity1.Distance(a)MinkowskiDistance(b)Stati