dragonstar_lecture4_linear_classification

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1、4.LinearClassificationKaiYuLinearClassifiers•Asimplestclassificationmodel•Helptounderstandnonlinearmodels•Arguablythemostusefulclassificationmethod!2LinearClassifiers•Asimplestclassificationmodel•Helptounderstandnonlinearmodels•Arguablythemostusefulclassificationmethod!3OutlinePerceptronAlgorithmSuppo

2、rtVectorMachinesLogisticRegressionSummary4BasicNeuron5PerceptronNode–ThresholdLogicUnitx1w1xwbz22xnwnn1if∑xiwi≥bi=1z=n0if∑xiwi

3、1z=.4.10n0if∑xiwi

4、iIterativelyapplyanexamplefromthetrainingsetEachiterationthroughthetrainingsetisanepochContinuetraininguntiltotaltrainingerrorislessthanepsilonPerceptronConvergenceTheorem:Guaranteedtofindasolutioninfinitetimeifasolutionexists10OutlinePerceptronAlgorithmSupportVectorMachinesLogisticRegressio

5、nSummary11SupportVectorMachines:Overview•Apowerfulmethodfor2-classclassification•Originalidea:Vapnik,1965forlinearclassifiers•SVM,CorteandVapnik,1995•Becomesveryhotsincelate90’s•Bettergeneralization(lessoverfitting)•Keyideas–Usekernelfunctiontotransformlowdimensionaltrainingsamplestohigherdim(forli

6、nearseparabilityproblem)–Usequadraticprogramming(QP)tofindthebestclassifierboundaryhyperplane(forglobaloptimaand)αLinearClassifiersxfyestf(x,w,b)=sign(w.x-b)denotes+1denotes-1Howwouldyouclassifythisdata?αLinearClassifiersxfyestf(x,w,b)=sign(w.x-b)denotes+1denotes-1Howwouldyouclassifythisdata?αLinearC

7、lassifiersxfyestf(x,w,b)=sign(w.x-b)denotes+1denotes-1Howwouldyouclassifythisdata?αLinearClassifiersxfyestf(x,w,b)=sign(w.x-b)denotes+1denotes-1Howwouldyouclassifythisdata?αLinearClassifiersxfyestf(x,w,b)=sign(w.x-b)denot