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).We wouldthenpredict\1"onaninputxif andonlyifh (x) 0:5, orequivalently, if andonlyif Tx trainingexample(y= 1).Thelarger Txis,thelargeralsoish (x) =p(y= 1jx;w; b), andthus alsothehigherourdegreeof \con dence"thatthelabel is 1.
, subject to each training example having func-tional margin at least . The jjwjj = 1 constraint moreover ensures that the functional margin equals to the geometric margin, so we are also guaranteed that all the geometric margins are at least . Thus, solving this problem will result in (w;b) with the largest possible geometric margin with ...
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