Using the Self-Organizing Map

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1、PAPERSUBMITTEDTOTHESPECIALISSUEOFIEEETNNONTEMPORALCODING1IdenticationandControlofDynamicalSystemsUsingtheSelf-OrganizingMapGuilhermeA.Barreto,member,IEEE,andAluizioF.R.AraujoAbstract

2、Inthispaper,weintroduceageneralmodelingforfunctionapproximation,insteadoftheusualsupe

3、r-technique,calledVector-QuantizedTemporalAssociativeMem-visedones(MLPandRBF).Thistechnique,calledVector-ory(VQTAM),whichusesKohonen'sSelf-OrganizingMapQuantizedTemporalAssociativeMemory(VQTAM),shows(SOM)asanalternativetoMLPandRBFneuralmodelsfordynamicalsystemidenticat

4、ionandcontrol.Wedemon-thattheSOMcanbesuccessfullyusedtoapproximatestratethattheestimationerrorsdecreaseastheSOMtrain-dynamicalinput-outputmappings,withminormodica-ingproceeds,allowingtheVQTAMschemetobeunderstoodtionsintheoriginalalgorithm.TheSOMisanunsuper-asaself-supe

5、rvisedgradient-basederrorreductionmethod.Theperformanceoftheproposedapproachisevaluatedonavisedneuralalgorithmdesignedtobuildarepresentationvarietyofcomplextasks,namely:(i)timeseriesprediction,ofneighborhood(spatial)relationshipsamongvectorsof(ii)identicationofSISO/MIM

6、Osystems,and(iii)nonlin-anunlabelleddataset.TheneuronsintheSOMareputearpredictivecontrol.Foralltasks,thesimulationresultstogetherinanoutputlayer,A,inone-,two-oreventhree-producedbytheSOMareasaccurateasthoseproducedbytheMLPnetwork,andbetterthanthoseproducedbythedimension

7、alarrays.Eachneuroni2Ahasaweightvec-RBFnetwork.TheSOMhasalsoshowntobelesssensitivetorw2

8、eirrelationshipstootherwell-establishedmethodsforcompetitive-cooperativeschemeinwhichtheweightvec-dynamicalsystemidentication.Wealsosuggestdirectionstorsofawinningneuronanditsneighborsintheoutputforfurtherwork.arrayareupdatedafterthepresentationofaninputvec-Keywords

9、Se

10、lf-organizingmaps,timedelays,temporaltor.Usually,atrainedSOMisusedforclusteringanddataassociativememory,functi