Neural Network Toolbox User's Guide

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Mean and Stand. Dev. (prestd, poststd, trastd) . . . . . . . . . . . . 5-62Principal Component Analysis (prepca, trapca) . . . . . . . . . . . . 5-63Post-Training Analysis (postreg) . . . . . . . . . . . . . . . . . . . . . . . . 5-64Sample Training Session . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-66Limitations and Cautions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-71Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-736Control SystemsIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-2NN Predictive Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-4System Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-4Predictive Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-5Using the NN Predictive Controller Block . . . . . . . . . . . . . . . . . 6-6NARMA-L2 (Feedback Linearization) Control . . . . . . . . . . 6-14Identification of the NARMA-L2 Model . . . . . . . . . . . . . . . . . . 6-14NARMA-L2 Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-16Using the NARMA-L2 Controller Block . . . . . . . . . . . . . . . . . . 6-18Model Reference Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-23Using the Model Reference Controller Block . . . . . . . . . . . . . . 6-25Importing and Exporting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-31Importing and Exporting Networks . . . . . . . . . . . . . . . . . . . . . 6-31Importing and Exporting Training Data . . . . . . . . . . . . . . . . . 6-35Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-38xxContents
7Radial Basis NetworksIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-2Important Radial Basis Functions . . . . . . . . . . . . . . . . . . . . . . . 7-2Radial Basis Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-3Neuron Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-3Network Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4Exact Design (newrbe) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-5More Efficient Design (newrb) . . . . . . . . . . . . . . . . . . . . . . . . . . 7-7Demonstrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-8Generalized Regression Networks . . . . . . . . . . . . . . . . . . . . . . 7-9Network Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-9Design (newgrnn) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-10Probabilistic Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . 7-12Network Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-12Design (newpnn) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-13Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-15Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-16New Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-188Self-Organizing and Learn. Vector Quant. NetsIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-2Important Self-Organizing and LVQ Functions . . . . . . . . . . . . . 8-2Competitive Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-3Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-3Creating a Competitive Neural Network (newc) . . . . . . . . . . . . 8-4Kohonen Learning Rule (learnk) . . . . . . . . . . . . . . . . . . . . . . . . . 8-5Bias Learning Rule (learncon) . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-5Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-6xxi
Page 1 and 2: Neural Network ToolboxFor Use with
Page 3: Printing History: June 1992 First p
Page 6 and 7: PrefaceNeural NetworksNeural networ
Page 8 and 9: PrefaceBasic ChaptersThe Neural Net
Page 10 and 11: PrefaceInput Weight MatrixLayer Wei
Page 12 and 13: PrefaceNeural Network Design BookPr
Page 14 and 15: PrefaceOrlando De Jesús of Oklahom
Page 16 and 17: Generalization and Speed Benchmarks
Page 18 and 19: Introduction to the GUI . . . . . .
Page 22 and 23: Graphical Example . . . . . . . . .
Page 24 and 25: 11ApplicationsIntroduction . . . .
Page 26 and 27: 14ReferenceFunctions — Categorica
Page 28 and 29: Block Generation . . . . . . . . .
Page 30 and 31: 1 IntroductionGetting StartedBasic
Page 32 and 33: 1 IntroductionNote We no longer rec
Page 34 and 35: 1 IntroductionDefense• Weapon ste
Page 36 and 37: 1 Introduction1-8
Page 38 and 39: 2 Neuron Model and Network Architec
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3 PerceptronsIntroductionThis chapt
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3 PerceptronsNeuron ModelA perceptr
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3 PerceptronsPerceptron Architectur
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3 Perceptronsgivesbiases = net.bias
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3 Perceptronswhich givesbias =0Now
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3 PerceptronsLearning RulesWe defin
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3 PerceptronsCASE 1. If e = 0, then
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3 PerceptronsTraining (train)If sim
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3 PerceptronsOn this occasion, the
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3 PerceptronsTRAINC, Epoch 0/20TRAI
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3 PerceptronsBy changing the percep
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3 PerceptronsClick on Help to get s
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3 PerceptronsNext you might look at
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3 PerceptronsThus, the network was
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3 Perceptrons2 1Similarly,ANDNet.b{
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3 Perceptronswindow. Select the Loa
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3 PerceptronsPerceptron Transfer Fu
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3 PerceptronsOne Perceptron NeuronI
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4 Linear FiltersIntroductionThe lin
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4 Linear FiltersNetwork Architectur
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4 Linear FiltersWe can create a net
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4 Linear FiltersMean Square ErrorLi
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4 Linear FiltersLinear Networks wit
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4 Linear Filtersnet = newlind(P,T,P
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4 Linear FiltersFinally, the change
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4 Linear FiltersWe will use train t
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4 Linear FiltersLimitations and Cau
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4 Linear FiltersSummarySingle-layer
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4 Linear FiltersLinear Network Laye
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4 Linear FiltersTapped Delay LineTD
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4 Linear FiltersFunctionlearnwhpure
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5 BackpropagationIntroductionBackpr
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5 BackpropagationFundamentalsArchit
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5 BackpropagationThe three transfer
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5 Backpropagationweights, but you m
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5 BackpropagationBatch Gradient Des
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5 BackpropagationMomentum can be ad
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5 BackpropagationFaster TrainingThe
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5 BackpropagationThe function train
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5 Backpropagationdifferent search f
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5 BackpropagationPolak-Ribiére Upd
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5 Backpropagation[net,tr]=train(net
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5 BackpropagationThis procedure is
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5 BackpropagationThe backtracking a
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5 BackpropagationTRAINOSS-srchbac,
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5 Backpropagationequation is a buil
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5 BackpropagationSpeed and Memory C
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5 BackpropagationAlgorithmMeanTime
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5 BackpropagationSpeed Comparison o
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5 BackpropagationComparsion of Conv
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5 BackpropagationThe following figu
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5 Backpropagationon pattern recogni
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5 BackpropagationTime Comparison on
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5 BackpropagationComparsion of Conv
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5 BackpropagationAlgorithmMeanTime
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5 Backpropagationnumber of weights.
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5 Backpropagationgeneralization tha
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5 Backpropagationp = [-1:.05:1];t =
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5 Backpropagationprocess. If the er
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5 Backpropagationtraining parameter
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5 BackpropagationBayesian regulariz
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5 Backpropagationaccomplished with
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5 Backpropagationpnewn = trastd(pne
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5 BackpropagationSample Training Se
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5 Backpropagation3.532.5TrainingVal
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5 Backpropagation120Best Linear Fit
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5 Backpropagationcorrect weights fo
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5 BackpropagationFunctiontraincgftr
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5 Backpropagation5-76
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6 Control SystemsIntroductionNeural
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NN Predictive ControlThe neural net
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NN Predictive Controlw 1 w 2C b1C b
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NN Predictive ControlThe File menu
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NN Predictive Control5 Select the G
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NN Predictive Controlplant output a
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NARMA-L2 (Feedback Linearization) C
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Model Reference ControlModel Refere
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Model Reference ControlUsing the Mo
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Model Reference ControlThe file men
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Model Reference Controlbecause the
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Importing and ExportingImporting an
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Importing and ExportingThis causes
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Importing and ExportingImporting an
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Importing and ExportingSelect MAT-f
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7Radial Basis NetworksIntroduction
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Radial Basis FunctionsRadial Basis
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Radial Basis FunctionsFortunately,
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Radial Basis Functionsacceptable so
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Generalized Regression NetworksGene
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Generalized Regression NetworksP =
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Probabilistic Neural NetworksThe se
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SummarySummaryRadial basis networks
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SummaryRadial Basis Network Archite
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SummaryFunctionnewpnnnewrbnewrbenor
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8Self-Organizing andLearn. Vector Q
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Competitive LearningCompetitive Lea
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Competitive LearningKohonen Learnin
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Competitive LearningThus, during ea
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Self-Organizing MapsSelf-Organizing
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Self-Organizing MapsHere neuron 1 h
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Self-Organizing Mapsplotsom(pos)to
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Self-Organizing Maps0 1 20 1 2We fi
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Self-Organizing MapsandP1= [1;1]P1
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Self-Organizing Maps2Weight Vectors
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Self-Organizing MapsLearning occurs
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Self-Organizing MapsWeight Vectors1
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Self-Organizing Maps1.51W(i,2)0.50-
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Self-Organizing Maps10.50-0.5-1-1 0
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Self-Organizing MapsAfter 120 cycle
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Learning Vector Quantization Networ
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SummaryFiguresCompetitive Network A
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SummaryFunctionnewlvqlearnlv1learnl
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9Recurrent NetworksIntroduction (p.
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Elman NetworksElman NetworksArchite
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Elman NetworksY = sim(net,Pseq)Y =C
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Elman NetworksT = [0 (P(1:end-1)+P(
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Hopfield Networka1(k-1) Dn1R 1pR 1
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Hopfield NetworkWe can execute the
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Hopfield Networkwhich givesW =0.692
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SummarySummaryElman networks, by ha
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SummaryNew FunctionsThis chapter in
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10Adaptive Filters andAdaptive Trai
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Linear Neuron ModelLinear Neuron Mo
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Adaptive Linear Network Architectur
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Mean Square ErrorMean Square ErrorL
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Adaptive Filtering (adapt)Adaptive
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Adaptive Filtering (adapt)InputLine
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Adaptive Filtering (adapt)bias = ne
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Adaptive Filtering (adapt)Pilot’s
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Adaptive Filtering (adapt)p(k)pd(k)
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SummaryPurelin Transfer Functiona0+
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SummaryLMS (Widrow-Hoff) AlgorithmT
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SummaryAdaptive Filter ExampleInput
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SummaryMultiple Neuron Adaptive Fil
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11ApplicationsIntroduction (p. 11-2
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Applin1: Linear DesignApplin1: Line
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Applin1: Linear Design1Output and T
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Applin2: Adaptive PredictionApplin2
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Applin2: Adaptive Prediction1.5Outp
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Appelm1: Amplitude DetectionAppelm1
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Appelm1: Amplitude DetectionThe fin
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Appelm1: Amplitude DetectionImprovi
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Appcr1: Character RecognitionPerfec
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Appcr1: Character RecognitionThen,
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Appcr1: Character Recognition50Perc
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12Advanced TopicsCustom Networks (p
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Custom NetworksTo create custom net
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Custom NetworksNote that net.numInp
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Custom NetworksSubobject Properties
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Custom Networksnet.layers{1}.initFc
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Custom Networkssize: 4userdata: [1x
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Custom Networksans =-0.3040 0.4703-
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Custom NetworksY =[3x1 double] [3x1
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Additional Toolbox FunctionsLearnin
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Custom Functionsoutput and net inpu
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Custom Functionsinput must have the
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Custom FunctionsTo be a valid weigh
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Custom FunctionsYour network initia
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Custom Functionsb = rands(S)where:
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Custom FunctionsWhen you set the ne
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Custom Functions• Tl is an N l ×
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Custom Functions- Each E{i,ts} is t
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Custom FunctionsWeight and Bias Lea
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Custom FunctionsOnce defined, you c
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Custom FunctionsTo be a valid dista
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13Network Object ReferenceNetwork P
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Network Propertiesnet.outputConnect
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Network PropertiesIt can be set to
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Network PropertiesInput Properties.
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Network Propertiesif the correspond
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Network PropertiesIt can be set to
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Network PropertiesThe fields of thi
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Network PropertiesLWThis property d
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Subobject PropertiesSubobject Prope
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Subobject Propertiesnet.layers{i}.d
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Subobject Propertiespositions (read
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Subobject PropertiesCustom function
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Subobject Propertiesnet.layers{i}.u
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Subobject PropertieslearnFcnThis pr
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Subobject PropertiesinitFcnThis pro
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Subobject Properties(net.trainFcn)
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Subobject PropertiesinitFcnThis pro
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Subobject Properties(net.trainFcn)
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14ReferenceFunctions — Categorica
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Functions — Categorical ListLearn
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Functions — Categorical ListNew N
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Functions — Categorical ListPre-
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Functions — Categorical ListTrans
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Functions — Categorical ListUtili
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Functions — Categorical ListWeigh
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Transfer Function Graphsa0+1-1a = l
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Transfer Function GraphsInput nOutp
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Functions — Alphabetical Listdtri
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Functions — Alphabetical Listplot
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adaptPurpose14adaptAllow a neural n
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adaptThe matrix format can be used
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oxdistPurpose14boxdistBox distance
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calcaHere the two initial layer del
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calca1Pc = [Pi P];Pd = calcpd(net,8
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calceHere we define the layer targe
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calce1[Ac,N,LWZ,IWZ,BZ] = calca(net
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calcgxnet.layerConnect(1,1) = 1;net
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calcjejjExamplesHere we create a li
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calcjxHere the two initial layer de
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calcperfPurpose14calcperfCalculate
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combvecPurpose14combvecCreate all c
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competTo model this type of layer e
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concurPurpose14concurCreate concurr
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dhardlimPurpose14dhardlimDerivative
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dispPurpose14dispDisplay a neural n
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distPurpose14distEuclidean distance
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dlogsigPurpose14dlogsigLog sigmoid
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dmsePurpose14dmseMean squared error
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dnetprodPurpose14dnetprodDerivative
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dotprodPurpose14dotprodDot product
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dpurelinPurpose14dpurelinLinear tra
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dsatlinPurpose14dsatlinDerivative o
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dssePurpose14dsseSum squared error
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dtribasPurpose14dtribasDerivative o
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formxPurpose14formxForm bias and we
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getxPurpose14getxGet all network we
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hardlimPurpose14hardlimHard limit t
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hardlimsPurpose14hardlimsSymmetric
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hextopPurpose14hextopHexagonal laye
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hintonwbPurpose14hintonwbHinton gra
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initPurpose14initInitialize a neura
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initconPurpose14initconConscience b
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initnwPurpose14initnwNguyen-Widrow
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initwbPurpose14initwbBy-weight-and-
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learnconPurpose14learnconConscience
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learncon(Note that learncon is able
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learngdExamples Here we define a ra
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learngdmlearngdm(code) returns usef
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learnhPurpose14learnhHebb weight le
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learnhdPurpose14learnhdHebb with de
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learnisPurpose14learnisInstar weigh
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learnkPurpose14learnkKohonen weight
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learnlv1Purpose14learnlv1LVQ1 weigh
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learnlv2Purpose14learnlv2LVQ2.1 wei
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learnlv2the input p is roughly equa
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learnosExamplesHere we define a ran
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learnpe = rand(3,1);Since learnp on
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learnpnPurpose14learnpnNormalized p
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learnpntargets of 1 cannot be separ
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learnsomlearnpn(code) returns usefu
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learnwhPurpose14learnwhWidrow-Hoff
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learnwhSee AlsoReferencesnewlin, ad
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logsigPurpose14logsigLog sigmoid tr
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maePurpose14maeMean absolute error
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mandistPurpose14mandistManhattan di
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maxlinlrPurpose14maxlinlrMaximum le
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minmaxPurpose14minmaxRanges of matr
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mseperf = mse(e)Note that mse can b
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mseregmsereg(code) returns useful i
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netprodPurpose14netprodProduct net
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networkPurpose14networkCreate a cus
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networkSubobject structure properti
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networknet.layers{1}.transferFcn =
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newcYc = vec2ind(Y)See Alsosim, ini
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newcfExamplesHere is a problem cons
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newelmExamples Here is a series of
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newffExamplesHere is a problem cons
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newfftdThe performance function can
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newgrnnSee AlsoReferencessim, newrb
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newhopIf you run the above code, Y{
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newlinP2 = {1 0 -1 -1 1 1 1 0 -1};T
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newlindT = {5.0 6.1 4.0 6.0 6.9 8.0
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newlvqThe target classes Tc are con
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newpHere we define a sequence of ta
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newpnnnewpnn sets the first layer w
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newrbsecond layer has purelin neuro
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newrbe[W{2,1} b{2}] * [A{1}; ones]
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newsomplotsom(net.layers{1}.positio
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nnt2cPurpose14nnt2cUpdate NNT 2.0 c
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nnt2ffPurpose14nnt2ffUpdate NNT 2.0
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nnt2linPurpose14nnt2linUpdate NNT 2
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nnt2pPurpose14nnt2pUpdate NNT 2.0 p
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nnt2somPurpose14nnt2somUpdate NNT 2
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normcPurpose14normcNormalize the co
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normrPurpose14normrNormalize the ro
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plotepPurpose14plotepPlot a weight-
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plotpcPurpose14plotpcPlot a classif
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plotpvPurpose14plotpvPlot perceptro
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plotvPurpose14plotvPlot vectors as
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pnormcPurpose14pnormcPseudo-normali
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poslinCall sim to simulate the netw
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postmnmxSee Alsopremnmx, prepca, po
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postregSee Alsopremnmx, prepca14-20
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poststdSee Alsopremnmx, prepca, pos
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prepcaPurpose14prepcaPrincipal comp
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prestd14prestdPurpose Preprocess da
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purelinTo change a network so a lay
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adbasPurpose14radbasRadial basis tr
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andncPurpose14randncNormalized colu
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andsPurpose14randsSymmetric random
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evertPurpose14revertChange network
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satlinCall sim to simulate the netw
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satlinsTo change a network so that
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setxPurpose14setxSet all network we
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simThe cell array format is easiest
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sim[y2,pf] = sim(net,p2,pf)Here new
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softmaxPurpose14softmaxSoft max tra
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srchbacPurpose14srchbacOne-dimensio
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srchbacp = [0 1 2 3 4 5];t = [0 0 0
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srchbrePurpose14srchbreOne-dimensio
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srchbreHere a two-layer feed-forwar
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srchchameanings for different searc
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srchgolPurpose14srchgolOne-dimensio
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srchgolhas one logsig neuron. The t
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srchhybmeanings for different searc
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ssePurpose14sseSum squared error pe
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sumsqrPurpose14sumsqrSum squared el
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tansigNetwork UseYou can create a s
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trainThe cell array format is easie
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trainy1 = sim(net,p)plot(p,t,'o',p,
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trainbTraining occurs according to
Page 717 and 718:
trainbfgPurpose14trainbfgBFGS quasi
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trainbfgnet.trainParam.low_lim0.1 L
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trainbfgTo prepare a custom network
Page 723 and 724:
trainbrPurpose14trainbrBayesian reg
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trainbrIf VV is not [], it must be
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trainbrThe adaptive value mu is inc
Page 729 and 730:
traincTraining occurs according to
Page 731 and 732:
traincgbPurpose14traincgbConjugate
Page 733 and 734:
traincgbDimensions for these variab
Page 735 and 736:
traincgbAlgorithmtraincgb can train
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traincgfTraining occurs according t
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traincgftraincgf(code) returns usef
Page 741 and 742:
traincgfReferencesScales, L. E., In
Page 743 and 744:
traincgpTraining occurs according t
Page 745 and 746:
traincgptraincgp(code) returns usef
Page 747 and 748:
traincgpReferencesScales, L. E., In
Page 749 and 750:
traingdTraining occurs according to
Page 751 and 752:
traingdaPurpose14traingdaGradient d
Page 753 and 754:
traingdaValidation vectors are used
Page 755 and 756:
traingdmPurpose14traingdmGradient d
Page 757 and 758:
traingdmtraingdm(code) returns usef
Page 759 and 760:
traingdxTraining occurs according t
Page 761 and 762:
traingdx• The maximum amount of t
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trainlmTraining occurs according to
Page 765 and 766:
trainlmwhere E is all errors and I
Page 767 and 768:
trainossTraining occurs according t
Page 769 and 770:
trainosstrainoss(code) returns usef
Page 771 and 772:
trainrPurpose14trainrRandom order i
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trainr3 Set each net.layerWeights{i
Page 775 and 776:
trainrpTraining occurs according to
Page 777 and 778:
trainrpNetwork UseYou can create a
Page 779 and 780:
trainsPurpose14trainsSequential ord
Page 781 and 782:
trainsTo allow the network to adapt
Page 783 and 784:
trainscgTraining occurs according t
Page 785 and 786:
trainscgNetwork UseYou can create a
Page 787 and 788:
tramnmxSee Alsopremnmx, prestd, pre
Page 789 and 790:
trapcaAlgorithmSee AlsoPtrans = tra
Page 791 and 792:
trastdSee Alsopremnmx, prepca, pres
Page 793 and 794:
tribasCall sim to simulate the netw
Page 795 and 796:
GlossaryA
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ias vector - A column vector of bia
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Fletcher-Reeves update - A method d
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local minimum - The minimum of a fu
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perceptron learning rule - A learni
Page 805 and 806:
symmetric hard-limit transfer funct
Page 807 and 808:
BibliographyB
Page 809 and 810:
discusses their current application
Page 811 and 812:
[LiMi89] Li, J., A. N. Michel, and
Page 813 and 814:
[RuHi86b] Rumelhart, D. E., G. E. H
Page 815 and 816:
Demonstrations andApplicationsC
Page 817 and 818:
Tables of Demonstrations and Applic
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Tables of Demonstrations and Applic
Page 821 and 822:
DSimulinkBlock Set (p. D-2)Block Ge
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Block SetEach of these blocks takes
Page 825 and 826:
Block GenerationBlock GenerationThe
Page 827 and 828:
Block GenerationNote that the outpu
Page 829 and 830:
ECode NotesDimensions (p. E-2)Varia
Page 831 and 832:
VariablesVariablesThe variables a u
Page 833 and 834:
VariablesIWZWeighted inputs.Ni-by-N
Page 835 and 836:
FunctionsFunctionsThe following fun
Page 837 and 838:
Argument CheckingArgument CheckingT
Page 839 and 840:
IndexAADALINE networkdecision bound
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IndexManhattan 8-16tuning phase 8-1
Page 843 and 844:
Indexlinear transfer function 2-3,
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IndexNNT block set D-2SimulinkNNT b
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