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1、1300IEEETRANSACTIONSONPATTERNANALYSISANDMACHINEINTELLIGENCE,VOL.19,NO.11,NOVEMBER1997JointInductionofShapeFeaturesandTreeClassifiersYaliAmit,DonaldGeman,andKennethWilderAbstract—Weintroduceaverylargefamilyofbinaryfeaturesfortwo-dimensionalshapes.Thesalientonesforseparatingp
2、articularshapesaredeterminedbyinductivelearningduringtheconstructionofclassificationtrees.Thereisafeatureforeverypossiblegeometricarrangementoflocaltopographiccodes.Thearrangementsexpresscoarseconstraintsonrelativeanglesanddistancesamongthecodelocationsandarenearlyinvariant
3、tosubstantialaffineandnonlineardeformations.Theyarealsopartiallyordered,whichmakesitpossibletonarrowthesearchforinformativeonesateachnodeofthetree.Differenttreescorrespondtodifferentaspectsofshape.Theyarestatisticallyweaklydependentduetorandomizationandareaggregatedinasimpl
4、eway.Adaptingthealgorithmtoashapefamilyisthenfullyautomaticoncetrainingsamplesareprovided.Asanillustration,weclassifyhandwrittendigitsfromtheNISTdatabase;theerrorrateis.7percent.IndexTerms—Shapequantization,featureinduction,invariantarrangements,multipledecisiontrees,random
5、ization,digitrecognition,localtopographiccodes.————————✦————————1INTRODUCTIONWErevisittheproblemoffindinggoodfeaturesforseparatingtwo-dimensionalshapeclassesinthecontextofinvarianceandinductivelearning.Thefeaturesetweconsiderisvirtuallyinfinite.Thesalientonesforaparticulars
6、hapefamilyaredeterminedfromtrainingsamplesduringtheconstructionofclassificationtrees.Weexperimentwithisolatedhandwrittendigits.Off-linerecognitionhasattractedenormousattention,includingacompetitionspon-soredbytheNationalInstituteofStandardsandTechnology(NIST)[1],andthereiss
7、tillnosolutionthatmatcheshumanper-formance.Manyapproachestodayarebasedonnonparametricstatisticalmethodssuchasneuralnetworks[2],[3],discriminantanalysis[4],[5],nearest-neighborruleswithdifferentmetrics[6],[7],[8],andclassificationtrees[9],[10].Hybridandmultipleclassi-fiersar
8、ealsoeffective[11],[12].Inmanycasesthefeaturevectordoesnotexplicitlyaddress“shape.
