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1、,,1–43()cKluwerAcademicPublishers,Boston.ManufacturedinTheNetherlands.ATutorialonSupportVectorMachinesforPatternRecognitionCHRISTOPHERJ.C.BURGESburges@lucent.comBellLaboratories,LucentTechnologiesAbstract.ThetutorialstartswithanoverviewoftheconceptsofV
2、Cdimensionandstructuralriskminimization.WethendescribelinearSupportVectorMachines(SVMs)forseparableandnon-separabledata,workingthroughanon-trivialexampleindetail.Wedescribeamechanicalanalogy,anddiscusswhenSVMsolutionsareuniqueandwhentheyareglobal.Wedesc
3、ribehowsupportvectortrainingcanbepracticallyimplemented,anddiscussindetailthekernelmappingtechniquewhichisusedtoconstructSVMsolutionswhicharenonlinearinthedata.WeshowhowSupportVectormachinescanhaveverylarge(eveninfinite)VCdimensionbycomputingtheVCdimensi
4、onforhomogeneouspolynomialandGaussianradialbasisfunctionkernels.WhileveryhighVCdimensionwouldnormallybodeillforgeneralizationperformance,andwhileatpresentthereexistsnotheorywhichshowsthatgoodgeneralizationperformanceisguaranteedforSVMs,thereareseveralar
5、gumentswhichsupporttheobservedhighaccuracyofSVMs,whichwereview.Resultsofsomeexperimentswhichwereinspiredbytheseargumentsarealsopresented.Wegivenumerousexamplesandproofsofmostofthekeytheorems.Thereisnewmaterial,andIhopethatthereaderwillfindthatevenoldmate
6、rialiscastinafreshlight.Keywords:SupportVectorMachines,StatisticalLearningTheory,VCDimension,PatternRecognitionAppearedin:DataMiningandKnowledgeDiscovery2,121-167,19981.IntroductionThepurposeofthispaperistoprovideanintroductoryyetextensivetutorialontheb
7、asicideasbehindSupportVectorMachines(SVMs).Thebooks(Vapnik,1995;Vapnik,1998)containexcellentdescriptionsofSVMs,buttheyleaveroomforanaccountwhosepurposefromthestartistoteach.Althoughthesubjectcanbesaidtohavestartedinthelateseventies(Vapnik,1979),itisonly
8、nowreceivingincreasingattention,andsothetimeappearssuitableforanintroductoryreview.Thetutorialdwellsentirelyonthepatternrecognitionproblem.Manyoftheideastherecarrydirectlyovertothecasesofregressionestimationandlinearoperatorinver
