第一章 贝叶斯分类算法.ppt

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1、SergiosTheodoridisKonstantinosKoutroumbasVersion2ACourseonPATTERNRECOGNITION1PATTERNRECOGNITIONTypicalapplicationareasMachinevisionCharacterrecognition(OCR)ComputeraideddiagnosisSpeechrecognitionFacerecognitionBiometricsImageDataBaseretrievalDataminingBi

2、onformaticsThetask:Assignunknownobjects–patterns–intothecorrectclass.Thisisknownasclassification.2Features:Thesearemeasurablequantitiesobtainedfromthepatterns,andtheclassificationtaskisbasedontheirrespectivevalues.Featurevectors:Anumberoffeaturesconst

3、itutethefeaturevectorFeaturevectorsaretreatedasrandomvectors.3Anexample:4Theclassifierconsistsofasetoffunctions,whosevalues,computedat,determinetheclasstowhichthecorrespondingpatternbelongsClassificationsystemoverviewsensorfeaturegenerationfeaturesele

4、ctionclassifierdesignsystemevaluationPatterns5Supervised–unsupervisedpatternrecognition:ThetwomajordirectionsSupervised:Patternswhoseclassisknowna-prioriareusedfortraining.Unsupervised:Thenumberofclassesis(ingeneral)unknownandnotrainingpatternsareavaila

5、ble.6CLASSIFIERSBASEDONBAYESDECISIONTHEORYStatisticalnatureoffeaturevectorsAssignthepatternrepresentedbyfeaturevectortothemostprobableoftheavailableclassesThatismaximum7Computationofa-posterioriprobabilitiesAssumeknowna-prioriprobabilitiesThisisal

6、soknownasthelikelihoodof8TheBayesrule(Μ=2)where9TheBayesclassificationrule(fortwoclassesM=2)GivenclassifyitaccordingtotheruleEquivalently:classifyaccordingtotheruleForequiprobableclassesthetestbecomes1011Equivalentlyinwords:DividespaceintworegionsProbabi

7、lityoferrorTotalshadedareaBayesianclassifierisOPTIMALwithrespecttominimisingtheclassificationerrorprobability!!!!12Indeed:MovingthethresholdthetotalshadedareaINCREASESbytheextra“grey”area.13TheBayesclassificationruleformany(M>2)classes:Givenclassifyittoi

8、f:SuchachoicealsominimizestheclassificationerrorprobabilityMinimizingtheaverageriskForeachwrongdecision,apenaltytermisassignedsincesomedecisionsaremoresensitivethanothers14ForM=2Definethelossmatrixpenaltytermfordecidingcla