Transcription of Part V Support Vector Machines
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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).
predict either 1 or 1 (cf. the perceptron algorithm), without rst going through the intermediate step of estimating the probability of y being 1 (which was what logistic regression did). 3 Functional and geometric margins Lets formalize the notions of the functional and geometric margins. Given a
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