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基于图形分析方法的函数型数据异常值检验实证研究.docx

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基于图形分析方法的函数型数据异常值检验实证研究 Abstract: Thedetectionofoutliersisavitalaspectinstatisticalanalysis,anditbecomesmorechallengingwhendatasetstaketheformofafunctionratherthantraditionalvectordata.Inthispaper,wepresentanempiricalstudyofdetectingfunctionaloutliersthroughgraph-basedanalysismethods.Wefirstintroducetheconceptoffunctionaldataandtraditionaloutlierdetectionmethods.Then,wefocusonthegraph-basedapproach,includingconstructingthegraph,definingdistancemetrics,andidentifyingoutliers.Wedemonstratetheeffectivenessofthisapproachonsimulateddataandareal-worlddatasetrelatedtotemperaturereadings.Theresultsshowthatthegraph-basedapproachachievedhighsensitivityandspecificityinidentifyingfunctionaloutliers. Introduction: Outlierdetectionisacriticalissueindataanalysis,withvariousapplicationssuchasqualitycontrol,frauddetection,andanomalydetection.Traditionaloutlierdetectionmethodsaremostlydesignedforvectordata,whereeachobservationisrepresentedasapointinap-dimensionalspace.However,inmanyreal-worldscenarios,datacouldbefunctional,i.e.,asetoffunctionsobservedoveraparticulardomain.Forexample,medicalimaging,geospatialdata,andenvironmentalmonitoringgeneratefunctionaldata. Functionaldataanalysis(FDA)hasemergedasanessentialtooltohandlefunctionaldata,anditincludestechniquessuchasfunctionalprincipalcomponentanalysis,functionalregressionanalysis,andfunctionaldataclustering.Outlierdetectioninfunctionaldataischallengingduetoitshighdimensionalityandcomplexstructures.Functionaldataoutlierscouldtakemanyformssuchasoverallshapedeviation,localcurvaturedeviation,amplitudedeviation,andphasedeviation. Inthispaper,wepresentanempiricalstudyofagraph-basedoutlierdetectionmethodforfunctionaldata.Themethodemploysgraph-basedrepresentations,metrics,andalgorithmstoidentifyfunctionaloutliers.Wefirstlyintroducefunctionaldataandtraditionaloutlierdetectionmethods.Then,wefocusongraph-basedoutlierdetectionmethods,includinggraphconstruction,distancemetrics,andoutlieridentification.Finally,wedemonstratetheeffectivenessofthemet