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1、LearningwithKernelsSch¨olkopfandSmola:LearningwithKernels—Con?dentialdraft,pleasedonotcirculate—2001/03/0220:32LearningwithKernelsbyBernhardSch¨olkopfAlexanderJ.SmolaTheMITPressCambridge,MassachusettsLondon,EnglandSch¨olkopfandSmola:LearningwithKernels—Con?dentialdraft,pleased
2、onotcirculate—2001/03/0220:32c2000MassachusettsInstituteofTechnologyAllrightsreserved.Nopartofthisbookmaybereproducedinanyformbyanyelectronicormechanicalmeans(includingphotocopying,recording,orinformationstorageandretrieval)withoutpermissioninwritingfromthepublisher.Printedand
3、boundintheUnitedStatesofAmericaLibraryofCongressCataloging-in-PublicationDataLearningwithKernels/byBernhardSch¨olkopf,AlexanderJ.Smola.p.cm.Includesbibliographicalreferencesandindex.ISBN0-xxx-xxxxx-x(alk.paper)1.Machinelearning.2.Algorithms.3.KernelfunctionsI.Sch¨olkopf,Bernha
4、rd.II.Smola,AlexanderJ.xxxx.x.xxx2000xxx.x’x–xxxx00.xxxxxCIPContents1ATutorialIntroduction11.1DataRepresentationandSimilarity...................11.2ASimplePatternRecognitionAlgorithm...............31.3SomeInsightsFromStatisticalLearningTheory............61.4HyperplaneClassi?er
5、s..........................101.5SupportVectorClassi?cation......................131.6SupportVectorRegression........................161.7KernelPrincipalComponentAnalysis.................181.8EmpiricalResultsandImplementations................19References22Index26Sch¨olkopfandSm
6、ola:LearningwithKernels—Con?dentialdraft,pleasedonotcirculate—2001/03/0220:321ATutorialIntroductionThischapterdescribesthecentralideasofsupportvector(SV)learninginanutshell.Itsgoalistoprovideanoverviewofthebasicconcepts.Oneoftheseconceptsisthatofakernel.Ratherthanimmediatelygo
7、ingintoOverviewmathematicaldetail,weintroducekernelsinformallyassimilaritymeasuresthatarisefromaparticularrepresentationofpatterns(Section1.1),anddescribeasimplekernelalgorithmforpatternrecognition(Section1.2).Followingthat,wereportsomebasicinsightsfromstatisticallearningtheor
8、y,themathematicaltheorythatunderliesthebasicideaofSVlearning(
