模式识别Chapter 6-4 Fisher LD.ppt

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1、1PatternRecognition北京交通大学电子信息工程学院2ContentsIntroductionSinglelayerneuralnetworksApplicationsinglelayerneuralnetworkMulti-layerneuralnetworks3ApplicationsinglelayerneuralnetworkProblemsofdimensionality--PrincipalComponentAnalysis(PCA)--FisherLinearDiscriminant(FLD)PolynomialNeuralNetw

2、ork(PNN)4ProblemsofdimensionalityDimensionalityreduction--PrincipalComponentAnalysis(PCA)--FisherLinearDiscriminant(FLD)5PCAfindscomponentsthatareusefulforrepresentingdata,thereisnoreasontoassumethatthesecomponentsmustbeusefulfordiscriminatingbetweendataindeferentclasses.PrincipalCo

3、mponentAnalysis(PCA)67FisherLinearDiscriminant(FLD)数据表示与数据分类PCA找到了在更低维空间的最精确的数据表示方法:--在最大方差的方向投影数据。但最大方差方向未必对于分类有用。8FisherLinearDiscriminant(FLD)Mainidea:findabestdirectionsuchthattheprojectionontothislinecanbeeasilyseparated.9FisherLinearDiscriminant(FLD)Supposethatwehaveasetofnd-d

4、imensionalsamples.inthesubsetlabeledinthesubsetlabeledIf,istheprojectionofthecorrespondingontoalineinthedirectionof.Findabestdirection10FisherLinearDiscriminant(FLD)Findabestdirectionwhichwillenableaccurateclassification.Ameasureoftheseparationbetweentheprojectedpointsisthedifferenc

5、eofthesamplemeans.11FisherLinearDiscriminant(FLD)Thesamplemeanfortheprojectedpointsisgivenby:12FisherLinearDiscriminant(FLD)Thesamplemeanfortheprojectedpointsisgivenby:WecanmakethisdifferenceaslargeaswewishmerelybyscalingW13FisherLinearDiscriminant(FLD)Definethescatterforprojectedsa

6、mples.14FisherLinearDiscriminant(FLD)Definethescatterforprojectedsamples.isanestimateofthevarianceofthepooleddata.iscalledwithin-classscatter.15FisherLinearDiscriminant(FLD)Definethescatterforprojectedsamples.:within-classscatter.CriterionfunctionofFisherlineardiscriminantis:16Fishe

7、rLinearDiscriminant(FLD)CriterionfunctionofFisherlineardiscriminantis:17FisherLinearDiscriminant(FLD)Definescattermatrices:18FisherLinearDiscriminant(FLD)Definescattermatrices:19FisherLinearDiscriminant(FLD)maximize20FisherLinearDiscriminant(FLD)GeneralizedRayleighquotientAvectorwth

8、atmaximizeJ()mustsa