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1、ATutorialonSupportVectorRegression∗AlexJ.Smola†andBernhardSch¨olkopf‡September30,2003AbstractAssuch,itisfirmlygroundedintheframeworkofstatisticallearningtheory,orVCtheory,whichhasbeendevelopedoverInthistutorialwegiveanoverviewofthebasicideasunder-thelastthreedecadesbyVapnikandChervonenkis[1974],lyi
2、ngSupportVector(SV)machinesforfunctionestimation.Vapnik[1982,1995].Inanutshell,VCtheorycharacterizesFurthermore,weincludeasummaryofcurrentlyusedalgo-propertiesoflearningmachineswhichenablethemtogener-rithmsfortrainingSVmachines,coveringboththequadraticalizewelltounseendata.(orconvex)programmingpar
3、tandadvancedmethodsforInitspresentform,theSVmachinewaslargelydevel-dealingwithlargedatasets.Finally,wementionsomemodifi-opedatAT&TBellLaboratoriesbyVapnikandco-workerscationsandextensionsthathavebeenappliedtothestandard[Boseretal.,1992,Guyonetal.,1993,CortesandVapnik,1995,SValgorithm,anddiscussthea
4、spectofregularizationfromaSch¨olkopfetal.,1995,Sch¨olkopfetal.,1996,Vapniketal.,SVperspective.1997].Duetothisindustrialcontext,SVresearchhasuptodatehadasoundorientationtowardsreal-worldapplications.InitialworkfocusedonOCR(opticalcharacterrecognition).1IntroductionWithinashortperiodoftime,SVclassifi
5、ersbecamecompeti-tivewiththebestavailablesystemsforbothOCRandobjectThepurposeofthispaperistwofold.Itshouldserveasaself-recognitiontasks[Sch¨olkopfetal.,1996,1998a,Blanzetal.,containedintroductiontoSupportVectorregressionforread-11996,Sch¨olkopf,1997].AcomprehensivetutorialonSVclas-ersnewtothisrapi
6、dlydevelopingfieldofresearch.OnthesifiershasbeenpublishedbyBurges[1998].Butalsoinre-otherhand,itattemptstogiveanoverviewofrecentdevelop-gressionandtimeseriespredictionapplications,excellentper-mentsinthefield.formancesweresoonobtained[M¨ulleretal.,1997,DruckerTothisend,wedecidedtoorganizetheessayasfo
7、llows.etal.,1997,Stitsonetal.,1999,MatteraandHaykin,1999].AWestartbygivingabriefoverviewofthebasictechniquesinsnapshotofthestateoftheartinSVlearningwasrecentlysections1,2,and3,plusashortsummarywithanumberoftakena
