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).
training example (x(i);y(i)), we de ne the functional margin of (w;b) with respect to the training example ^ (i)= y (wTx+b): Note that if y(i) = 1, then for the functional margin to be large (i.e., for our prediction to be con dent and correct), then we need wTx+b to be a large positive number. Conversely, if y(i) = 1, then for the functional ...
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