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1、Real-ValuedPatternRecallbyAssociativeMemoryHumbertoSossa,RicardoBarrón,andJoséL.OropezaCentrodeInvestigaciónenComputación-IPN,Av.JuandeDiosBátiz,esquinaconMiguelOthóndeMendizábal,MexicoCity,07738.MexicoAbstract.Inthisnote,weintroduceanassociativememoryusefultorecallreal-valuedpatternsalteredwithmixe
2、dnoise(additiveandsubtractive).Numericalandrealexamplesaregiventoshowtheeffectivenessoftheproposal.Conditionsunderwhichtheproposedmemoriesareabletorecallpatternseitherfromthefundamentalsetofpatternsandfromdistortedversionsofthemarealsogiven.1IntroductionHumansareabletorecallpatternswithagreatfacilit
3、y.Tryingtoimplementthisabilityintoacomputerhasbeenamajortopicamongthecomputervisioncommunity.Severalapproacheshavebeenproposedtogiveasolutiontothisimportantproblem.Oneapproachisbasedontheso-calledneuralnetworks.Anassociativememory(AM)isakindofneuralnetwork.Itisadevicespeciallydesignedtorecallpattern
4、s.AnassociativememoryMcanbeviewedasaninput-outputsystemasfollows:x→M→y,withxandy,respectivelytheinputandoutputpatternsvectors.Eachinputvectorformsanassociationwithacorrespondingoutputvector.Anassociationbetweeninputpatternxandoutputpatternyisdenotedas()x,y.Forkintegerandkkpositive,thecorrespondingas
5、sociationwillbedenotedas()xy,.TheassociativememoryMisrepresentedbyamatrixwhoseij-thcomponentismij.Misgeneratedfromafiniteapriorisetofknownassociations,knownasthefundamentalsetofassociations,orsimplythefundamentalset(FS).Ifξisanindex,thefundamentalsetξξisrepresentedas:{(x,y)
6、ξ=,2,1K,p}withpthecardina
7、lityoftheset.Thepatternsthatformthefundamentalsetarecalledfundamentalpatterns.Ifitholdsthatξξ{}x=y∀ξ∈,2,1Kp,Misauto-associative,otherwiseitishetero-associative.Adistortedversionofapatternxtoberecuperatedwillbedenotedas~x.Ifwhenwfeedingadistortedversionofxwithw∈{},2,1K,ptoanassociativememorywM,ithapp
8、ensthattheoutputcorrespondsexactlytotheassociatedpatterny,wesaythatrecallingisperfect.Severalmodelsforassociativememorieshaveemergedinthelast40years.Referforexampleto[1-11].Worksreportedin[6],[8]and[1
