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ID:37582720
大小:315.38 KB
页数:19页
时间:2019-05-25
《Support Vector Machines Explained》由会员上传分享,免费在线阅读,更多相关内容在行业资料-天天文库。
1、March1,2009SupportVectorMachinesExplainedTristanFletcherwww.cs.ucl.ac.uk/sta/T.Fletcher/IntroductionThisdocumenthasbeenwritteninanattempttomaketheSupportVectorMachines(SVM),initiallyconceivedofbyCortesandVapnik[1],assim-pletounderstandaspossibleforthosewithminimalexperience
2、ofMachineLearning.Itassumesbasicmathematicalknowledgeinareassuchascal-culus,vectorgeometryandLagrangemultipliers.ThedocumenthasbeensplitintoTheoryandApplicationsectionssothatitisobvious,afterthemathshasbeendealtwith,howtoactuallyapplytheSVMforthedierentformsofproblemthateac
3、hsectioniscentredon.Thedocument'srstsectiondetailstheproblemofclassicationforlinearlyseparabledataandintroducestheconceptofmarginandtheessenceofSVM-marginmaximization.ThemethodologyoftheSVMisthenextendedtodatawhichisnotfullylinearlyseparable.ThissoftmarginSVMintroducesthei
4、deaofslackvariablesandthetrade-obetweenmaximizingthemarginandminimizingthenumberofmisclassiedvariablesinthesecondsection.ThethirdsectiondevelopstheconceptofSVMfurthersothatthetechniquecanbeusedforregression.ThefourthsectionexplainstheothersalientfeatureofSVM-theKernelTrick
5、.ItexplainshowincorporationofthismathematicalsleightofhandallowsSVMtoclassifyandregressnonlineardata.OtherthanCortesandVapnik[1],mostofthisdocumentisbasedonworkbyCristianiniandShawe-Taylor[2],[3],Burges[4]andBishop[5].Foranycommentsonorquestionsaboutthisdocument,pleasecontac
6、ttheauthorthroughtheURLonthetitlepage.AcknowledgmentsTheauthorwouldliketothankJohnShawe-TaylorandMartinSewellfortheirassitanceincheckingthisdocument.11LinearlySeparableBinaryClassication1.1TheoryWehaveLtrainingpoints,whereeachinputxihasDattributes(i.e.isofdimensionalityD)an
7、disinoneoftwoclassesyi=-1or+1,i.eourtrainingdataisoftheform:fx;ygwherei=1:::L;y2f 1;1g;x22.Thishyperplanecanbedescrib
8、edbywx+b=0where:wisnormaltothehyperplane.bistheperpendiculardistancefrom
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