BP神经网络模型推导.docx

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1、Theprojectdescribesteachingprocessofmulti-layerneuralnetworkemploying backpropagation algorithm.Toillustratethisprocessthethreelayerneuralnetworkwithtwoinputsandoneoutput,whichisshowninthepicturebelow,isused: Eachneuroniscomposedoftwounits.Firstunitaddsproductsofweig

2、htscoefficientsandinputsignals.Thesecondunitrealisenonlinearfunction,calledneuronactivationfunction.Signal e isadderoutputsignal,and y=f(e) isoutputsignalofnonlinearelement.Signal y isalsooutputsignalofneuron. Toteachtheneuralnetworkweneedtrainingdataset.Thetrainingd

3、atasetconsistsofinputsignals(x1 and x2 )assignedwithcorrespondingtarget(desiredoutput) z.Thenetworktrainingisaniterativeprocess.Ineachiterationweightscoefficientsofnodesaremodifiedusingnewdatafromtrainingdataset.Modificationiscalculatedusingalgorithmdescribedbelow:Ea

4、chteachingstepstartswithforcingbothinputsignalsfromtrainingset.Afterthisstagewecandetermineoutputsignalsvaluesforeachneuronineachnetworklayer.Picturesbelowillustratehowsignalispropagatingthroughthenetwork,Symbols w(xm)n representweightsofconnectionsbetweennetworkinpu

5、t xm andneuron n ininputlayer.Symbols yn representsoutputsignalofneuron n. Propagationofsignalsthroughthehiddenlayer.Symbols wmn representweightsofconnectionsbetweenoutputofneuron m andinputofneuron n inthenextlayer. Propagationofsignalsthroughtheoutputlayer. Inthene

6、xtalgorithmsteptheoutputsignalofthenetwork y iscomparedwiththedesiredoutputvalue(thetarget),whichisfoundintrainingdataset.Thedifferenceiscallederrorsignal d ofoutputlayerneuron. Itisimpossibletocomputeerrorsignalforinternalneuronsdirectly,becauseoutputvaluesofthesene

7、uronsareunknown.Formanyyearstheeffectivemethodfortrainingmultiplayernetworkshasbeenunknown.Onlyinthemiddleeightiesthebackpropagationalgorithmhasbeenworkedout.Theideaistopropagateerrorsignal d (computedinsingleteachingstep)backtoallneurons,whichoutputsignalswereinputf

8、ordiscussedneuron. Theweights'coefficients wmn usedtopropagateerrorsbackareequaltothisusedduringcomputingoutputvalue.Onlythedirecti