艾伯特A Tutorial on Support Vector Machines for Pattern Recognition

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1、DataMiningandKnowledgeDiscovery,2,121–167(1998)°c1998KluwerAcademicPublishers,Boston.ManufacturedinTheNetherlands.ATutorialonSupportVectorMachinesforPatternRecognitionCHRISTOPHERJ.C.BURGESburges@lucent.comBellLaboratories,LucentTechnologiesEditor:UsamaFayyadAbstract.Thetutor

2、ialstartswithanoverviewoftheconceptsofVCdimensionandstructuralriskminimization.WethendescribelinearSupportVectorMachines(SVMs)forseparableandnon-separabledata,workingthroughanon-trivialexampleindetail.Wedescribeamechanicalanalogy,anddiscusswhenSVMsolutionsareuniqueandwhenthe

3、yareglobal.Wedescribehowsupportvectortrainingcanbepracticallyimplemented,anddiscussindetailthekernelmappingtechniquewhichisusedtoconstructSVMsolutionswhicharenonlinearinthedata.WeshowhowSupportVectormachinescanhaveverylarge(eveninfinite)VCdimensionbycomputingtheVCdimensionfor

4、homogeneouspolynomialandGaussianradialbasisfunctionkernels.WhileveryhighVCdimensionwouldnormallybodeillforgeneralizationperformance,andwhileatpresentthereexistsnotheorywhichshowsthatgoodgeneralizationperformanceisguaranteedforSVMs,thereareseveralargumentswhichsupporttheobser

5、vedhighaccuracyofSVMs,whichwereview.Resultsofsomeexperimentswhichwereinspiredbytheseargumentsarealsopresented.Wegivenumerousexamplesandproofsofmostofthekeytheorems.Thereisnewmaterial,andIhopethatthereaderwillfindthatevenoldmaterialiscastinafreshlight.Keywords:supportvectormac

6、hines,statisticallearningtheory,VCdimension,patternrecognition1.IntroductionThepurposeofthispaperistoprovideanintroductoryyetextensivetutorialonthebasicideasbehindSupportVectorMachines(SVMs).Thebooks(Vapnik,1995;Vapnik,1998)containexcellentdescriptionsofSVMs,buttheyleaveroom

7、foranaccountwhosepurposefromthestartistoteach.Althoughthesubjectcanbesaidtohavestartedinthelateseventies(Vapnik,1979),itisonlynowreceivingincreasingattention,andsothetimeappearssuitableforanintroductoryreview.Thetutorialdwellsentirelyonthepatternrecognitionproblem.Manyofthei

8、deastherecarrydirectlyovertothecasesofregressionestimationandlinearoperator