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1、MachineLeaming,20,273-297(1995)~)1995KluwerAcademicPublishers,Boston.ManufacturedinTheNetherlands.Support-VectorNetworksCORINNACORTEScorinna@neurai.att.comVLADIMIRVAPNIKvlad@neurai.att.comAT&TBellLabs.,Hohndel,NJ07733,USAEditor:LorenzaSaittaAbstract.Thesupport-vect
2、ornetworkisanewleamingmachinefortwo-groupclassificationproblems.Themachineconceptuallyimplementsthefollowingidea:inputvectorsarenon-linearlymappedtoaveryhigh-dimensionfeaturespace.Inthisfeaturespacealineardecisionsurfaceisconstructed.Specialpropertiesofthedecisions
3、urfaceensureshighgeneralizationabilityofthelearningmachine.Theideabehindthesupport-vectornetworkwaspreviouslyimplementedfortherestrictedcasewherethetrainingdatacanbeseparatedwithouterrors.Wehereextendthisresulttonon-separabletrainingdata.Highgeneralizationabilityof
4、support-vectornetworksutilizingpolynomialinputtransformationsisdemon-strated.Wealsocomparetheperformanceofthesupport-vectornetworktovariousclassicallearningalgorithmsthatalltookpartinabenchmarkstudyofOpticalCharacterRecognition.Keywords:patternrecognition,efficient
5、learningalgorithms,neuralnetworks,radialbasisfunctionclassifiers,polynomialclassifiers.1.IntroductionMorethan60yearsagoR.A.Fisher(Fisher,1936)suggestedthefirstalgorithmforpatternrecognition.Heconsideredamodeloftwonormaldistributedpopulations,N(mt,~1)andN(m2,~2)ofnd
6、imensionalvectorsxwithmeanvectorsmlandm2andco-variancematricesEtandE2,andshowedthattheoptimal(Bayesian)solutionisaquadraticdecisionfunction:[~1IE2I](1)Fsq(X)=sign(x-ml)7"E~-~(x-ma)-~(x-m2):rEfl(x-m2)+In1-~11_]"InthecasewhereE1=Ez=~thequadraticdecisionfunction(1)deg
7、eneratestoalinearfunction:Flin(X)=sign[(mt-m2)T~i-lx-l(mlr~-lml2--mT~-lm2)].(2)Toestimatethequadraticdecisionfunctiononehastodetermine~freeparameters.Toestimatethelinearfunctiononlynfreeparametershavetobedetermined.Inthecasewherethenumberofobservationsissmall(sayle
8、ssthan10n2)estimatingo(nz)parametersisnotreliable.Fisherthereforerecommended,eveninthecaseof~1~~32,tousethelineardiscriminatorfunction(2)with~oft
