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1、IEEETRANSACTIONSONSIGNALPROCESSING,VOL.43,NO.6.JUNE19951485WaveletNeuralNetworksforFunctionLearningJunZhang,Member,IEEE,GilbertG.Walter,YuboMiao,andWanNgaiWayneLee,Member,IEEEAbshurct-Inthispaper,awavelet-basedneuralnetworkisnetworkscanbemucheasierthanMPLnetworks.Hence,describe
2、d.Thestructureofthisnetworkissimilartothatofthetherehasbeenconsiderableinterestintheimplementationofradialbasisfunction(RBF)network,exceptthatheretheradialRBFnetworks[3]-[5](alsoseethereferencesin[8])andthebasisfunctionsarereplacedbyorthonormalscalingfunctionsthattheoreticalana
3、lysisoftheirproperties,suchasapproximationarenotnecessarilyradial-symmetric.Theefficacyofthistypeofnetworkinfunctionlearningandestimationisdemonstratedabilityandconvergencerates[6]-[ti].throughtheoreticalanalysisandexperimentalresults.Inpartic-Fromthepointofviewoffunctionrepres
4、entation,anRBFular,ithasbeenshownthatthewaveletnetworkhasuniversalnetworkisaschemethatrepresentsafunctionofinterestbyandL2approximationpropertiesandisaconsistentfunctionusingmembersofafamilyofcompactly(orlocally)supportedestimator.Convergenceratesassociatedwiththesepropertiesba
5、sisfunctions.Thelocalityofthebasisfunctionsmakesareobtainedforcertainfunctionclasseswheretheratesavoidthe“curseofdimensionality.”Intheexperiments,thewavelettheIU3FnetworkmoresuitableinlearningfunctionswithnetworkperformedwellandcomparedfavorablytotheMLPlocalvariationsanddiscont
6、inuities.Furthermore,theRBFandRBFnetworks.networkscanrepresentanyfunctionthatisinthespacespannedbythefamilyofbasisfunctions.However,thebasisI.INTRODUCTIONfunctionsinthefamilyaregenerallynotorthogonalandareredundant.Thismeansthatforagivenfunction,itsRBFEVELOPINGMODELSfromobserve
7、ddata,orfunc-Dnetworkrepresentationisnotuniqueandisprobablynottionlearning,isafundamentalprobleminmanyfields,themostefficient.Inthiswork,wereplacethefamilyofsuchasstatisticaldataanalysis,signalprocessing,control,basisfunctionsfortheRBFnetworkbyanorthonormalbasis,forecasting,and
8、artificialintelligence.Thisproblemisalsonamely,thescal
