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1、ResearchonKernelFunctionofSupportVectorMachineLiuLijuam,ShenBoi,WangXing2(1.SchoolofElectronicandInformationEngineering,BeijingJiaotongUniversity,Beijing100044;2.ChinaInformationTechnologySecurityEvaluationCenter,Beijing100085)Abstract:SupportVectorMachineisakindofalgori
2、thmusedforclassifyinglinearandnonlineardata,whichnotonlyhasasolidtheoreticalfoundation,butismoreaccuratethanothersortingalgorithmsinmanyareasofapplications,especiallyindealingwithhigh-dimensionaldata.11isnotnecessaryforustogetthespecificmappingfunctioninsolvingquadratico
3、ptimizationproblemofSVM,andtheonlythingweneedtodoistousekernelfunctiontoreplacethecomplicatedcalculationofthedotproductofthedataset,reducingthenumberofdimensioncalculation・Thispaperintroducesthetheoreticalbasisofsupportvectormachine,summarizestheresearchstatusandanalyses
4、theresearchdirectionanddevelopmentprospectsofkernelfunction.Keywords:supportvectormachine;high-dimensiondata;kernelfunction;quadraticoptimization0IntroductionSupportvectormachine(SVM)wasintroducedintothefieldofmachinelearninganditsrelatedareain1992[1],havingreceivedwides
5、preadattentionofresearchersinlatertimeandhasmadegreatprogressinmanyfields.Itusesanonlinearmappingtomaporiginaltrainingdataintohigh-dimensionaldataspaceinordertofindtheoptimalclassificationhyperplaneseparatingthosedatabelongingtodifferentcategories・Supportvectormachineisb
6、asedonSLT(statisticallearningtheory)[2,3]VCdimensiontheoryandstructuralriskminimizationprinciple.Comparedwithtraditionalneuralnetworks,supportvectormachinegainsgreatenhancementingeneralizationabilityandovercomessomeproblemsexistinginfeed-forwardneuralnetworks,suchaslocal
7、minimumandthecurseofdimensionality[4].Theintroductionofkernelfunctiongreatlysimplifiesthecomplexityofdotproductoperationinsupportvectormachinefornonlineardataclassification,anditcanbeusedtodistinguishandenlargetheusefulfeatures,andsupportvectormachinebasedonkernelfunctio
8、nisplayingapowerfulroleinthefieldofdatamining.1SupportVectorMachineIfthetrainingdatasetislinearseparabl
