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375Vol.37,No.520115ACTAAUTOMATICASINICAMay,2011111,,,(Energyarti¯cialneuron,EAN),.,,(EANbasedself-growingandself-organizingneuralnetwork,ESGSONN),ESGSONN,.ESGSONN.16(RitterandKohonen,1989)ESGSONN,SOFMGCSESGSONN.,ESGSONN.,,,,,,DOI10.3724/SP.J.1004.2011.00615AnEnergyArti¯cialNeuronModelBasedSelf-growingandSelf-organizingNeuralNetworkBANXiao-Juan1LIUHao1XUZhuo-Ran1AbstractInthispaper,weestablishedanewarti¯cialneuronmodelcalledEAN(energyarti¯cialneuron)basedontheenergyconceptfromtheglialcellsaccordingtotherecentachievementsintheneuroscience¯eld.WesuggestedawaytodemonstrateEANmodelinmathematics.Inaddition,werealizedaself-growingandself-organizingneuralnetworkbasedontheEANmodelcalledESGSONN(EANbasedself-growingandself-organizingneuralnetwork).ESGSONNconsiderstheenergyinEAN,theentropyproductionsinthenetworkandthesimilarity(betweenthesampleandneurons0weights)asitsconditionsofgrowingandcompetitions.Itsmainfeaturesaredescribedasbelow:rapidgrowing,probabilitydensitypreservingandfewsuper°uousneurons.Aclassicalexperimentof16-kindanimals(afterRitterandKohonen,1989)provedESGSONNcanworkcorrectly.WeshowedthenewfeaturesofESGSONNbycomparingitwiththetraditionalself-organizingnetworkssuchasSOFMandGCS.Finally,wearguedabouttheessenceofthisnetworkinthehigh-dimensionalspace.KeywordsSelf-organizing,growingnetwork,energyarti¯cialneuron(EAN),unsupervisedleaning,high-dimensionalspace,entropy,clustering,2070,[1].:,2010-08-032010-12-27ManuscriptreceivedAugust3,2010;acceptedDecember27,2010(863)(2009AA062800,2009AA04Z163),(60973063),(4092028),(FRF-TP-09-016B)SupportedbyNationalHighTechnologyResearchandDe-velopmentProgramofChina(863Program)(2009AA062800,2009AA04Z163),NationalNaturalScienceFoundationofChina(60973063),BeijingNaturalScienceFoundation(4092028),andFundamentalResearchFundsfortheCentralUniversities(FRF-TP-09-016B)1.1000831.InformationSchoolofEngineering,UniversityofScienceandTechnologyBeijing,Beijing1000831982Kohonen(Self-organizingfeaturemaps,SOFM)[2¡3];,Fritzke(Growingcellstructure,GCS)[4](Growinggrid,GG)[5](Growingneuralgas,GNG)[6].GCSSOFM,SOFM,.,,,GNGNG,,,,Choi(Self-creatingandorganizingneuralnetworks,SCONN)[7],Martinetz(Neuralgas,NG)[8],61637,,,,,Blackmore(Incrementalgridgrowing,IGG)[9],,,,,,,Chow(Cell-splittinggrid,CSG)[10],,,;AlahakoonIGG(Dynamicself-organizingmap,DSOM)[11],Shen(Self-organizingin-crementalneuralnetwork,SOINN)[12¡14](Enhancedself-organizingincrementalneuralnetwork,ESOINN)[15].,,NP.,:1),,,;2)(Meanquantizationerror,MQE),,;3)S&P.,,,.,,|ESGSONN,ESGSONN,.,ESGSONN.1(EAN)1.1:.,,.1997,PfriegerBarresScience,[16],NatureScience,Ullian,[17],Song[18],Slezak[19].,,[20¡21](),[22¡23],,1(Astrocyte).1[20]Fig.1Anastrocytebetweentwoneurons[20],,.,[24].1.2(EAN),M-P[25],,(Energyarti¯cialneuron,EAN).EAN,.,,,5:617.1.(EAN):EAN=hXXX;OOO;M;I;F;EAN;LANi:XXX,XXX=[x1;¢¢¢;xn]T;OOO,OOO=fo(t)g;M,M=MW[ML,,MW=fug,ML=fw=fwigni=1;bg;I,I:u(t)=I()=(t);F,F:o(t)=F(u(t)¡µ);EAN;LANHebb.(EAN)2.2(EAN)Fig.2ThestructureoftheEANmodel2.:EAN=EconsumptionAN[EoverplusAN,EconsumptionAN=feijji;j=1;2;¢¢¢;mg,eijt,ijt+1,EoverplusAN.3.2EconsumptionAN,:eij=ij£¹e,,¹e,ijij,ij,We=2666641112¢¢¢1j2122¢¢¢2j............i1i2¢¢¢ij377775.EoverplusAN.,(1):EAN=¹e£ÃnXi;j=1ij+mXi;j=10ij!(1)1.8ijij£¹e·EoverplusAN,,9ijEoverplusANij£¹e,ij.2.,,,.2ESGSONN:2.1ESGSONNESGSONN().ESG-SONNt,,,.,,,.ESGSONN:4...GunitAN,GunitANWGt+14HunitG(t+1),:EANunit=hGunitAN;WG;4HunitG(t+1)i,GunitAN=hVc;Eci,Vc=fEANiji=1;2;¢¢¢,6gEAN,Ec=feijji;j=1,2,¢¢¢,6g,eijEANiEANj,WG6,12,.,4,1,8EANi2EANunit:EAN=Econsumption(i)AN[Eoverplus(i)AN=4We=26641¢¢¢1.........1¢¢¢13775EANunit4HunitG(t+1)EAN,(2):4HunitG(t+1)=¡XR2S(R)p(Rt+1)log2p(Rt+1)(2)61837,p(Rt+1)t.3.3Fig.3Neuronunittopologicalgraph5..,:G0=hVG;EGi,VG=fEANi;EANj;¢¢¢;EANkgEANiEANi,EG=feijji;j=1;2;¢¢¢;kg,eijEANiEANj.G0,G0,G0.:8EANi2G0:nXi=1¹e£ijEoverplusANG0½Gt^GunitAN(t+1)½GunitAN,Gt,GunitAN(t+1)t+1.3.,.,G04EunitAN=nPi=14Econsumption(i)AN=nPi;j=1¹e£ij,4Econsumption(i)AN,nG0.54EunitAN=nPi=14Econsumption(i)AN=n6.G0optimal.tn,G0t+14HunitG(t+1),G0:4HunitG0optimal(t+1)·4HunitG0i(t+1)kXXX¡¡[i=1G0j,G0it.7..EANunit,34,,:EANunit3=hGunit3AN;WG;4Hunit3G(t+1)iEANunit313,,4.4Fig.4Trebleneuronunittopologicalgraph8..EANcEANunit3,EANcEANunit3.147,,.9..,.EAN:k¡XXXik·»,».».1.t,G0type1,G0type2,G0type1:G0type1:G0type2:G0type2,5,,t+1,G0type1G0type2,:5:619(a)t(a)Twotypesofgrowingpointsatthemomentoft(b)G0type1t+1(b)ThenetworkaftergrownatG0type1(c)G0type2t+1(c)ThenetworkaftergrownatG0type25tt+1Fig.5Twotypesofgrowingpointatthemomentoftandtheirtopologicalgraphsaftergrowingatthemomentoft+14HG0type1(t+1)4HG0type2(t+1).m,nG0type1G0type2t,:4HG0type1(t+1)=¡0@Xi2type11XiPmXmlog2XiPmXm+Xj2type21XjPmXmlog2XjPmXm1A4HG0type2(t+1)=¡0@Xi2type12XiPnXnlog2XiPnXn+Xj2type22XjPnXnlog2XjPnXn1A,:4HG0type2(t+1)¡4HG0type1(t+1)=Xi2mXiPmXmlog2XiPmXm¡Xj2nXjPnXnlog2XjPnXn=mX1mlog21m¡nX1nlog21n=log2n¡log2mG0type1,,G0type1G0type2,,G0type1mG0type2n,mn,4HG0type1(t+1)4HG0type2(t+1)¤1,,,,,t+1.2.2ESGSONNESGSONN3:1);2);3).6.6Fig.6Thegrowingprocedureo