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Part V Support Vector Machines

CS229 LecturenotesAndrewNgPartVSupportVectorMa chinesThissetof notespresents theSupportVectorMachine(SVM) (andmany believe is indeedthebest)\o -the-shelf" telltheSVMstory, we'llneedto rsttalkaboutmarginsandtheideaof separatingdatawitha large\gap."Next,we'lltalkabouttheoptimal marginclassi er,which willleadus into a digressiononLagrangeduality. We'llalsoseekernels,which givea way to applySVMse cientlyin veryhighdimensional(such as in nite-dimensional)featurespaces,and nally, we'llcloseo thestorywiththeSMOalgorithm,which gives ane cient implementationof :IntuitionWe'llstartourstoryonSVMsby theintuitionsaboutmarginsandaboutthe\con dence"of ourpredic-tions;theseideaswillbe madeformalin ,wheretheprobabilityp(y= 1jx; ) is mod-eledbyh (x) =g( Tx).

We’ll also see kernels, which give a way to apply SVMs e ciently in very high dimensional (such as in nite-dimensional) feature spaces, and nally, we’ll close o the story with the SMO algorithm, which gives an e cient implementation of SVMs. 1 Margins: Intuition

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