Neural Network Toolbox User's Guide

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PrefaceBasic ChaptersThe Neural Network Toolbox is written so that if you read Chapter 2, Chapter3 and Chapter 4 you can proceed to a later chapter, read it and use its functionswithout difficulty. To make this possible, Chapter 2 presents the fundamentalsof the neuron model, the architectures of neural networks. It also will discussnotation used in the architectures. All of this is basic material. It is to youradvantage to understand this Chapter 2 material thoroughly.The neuron model and the architecture of a neural network describe how anetwork transforms its input into an output. This transformation can beviewed as a computation. The model and the architecture each placelimitations on what a particular neural network can compute. The way anetwork computes its output must be understood before training methods forthe network can be explained.viii
Mathematical Notation for Equations and FiguresMathematical Notation for Equations and FiguresBasic ConceptsScalars-small italic letters.....a,b,cVectors - small bold non-italic letters.....a,b,cMatrices - capital BOLD non-italic letters.....A,B,CLanguageVector means a column of numbers.Weight MatricesScalar Element w i, j () ti - row, j - column, t - time or iterationMatrixW()tColumn Vectorw j () tRow VectorBias Vectorw i() t...vector made of ith row of weight matrix WScalar Elementb i () tVectorb()tLayer NotationA single superscript is used to identify elements of layer. For instance, the netinput of layer 3 would be shown as n 3 .Superscripts k,l are used to identify the source (l) connection and thedestination (k) connection of layer weight matrices ans input weight matrices.For instance, the layer weight matrix from layer 2 to layer 4 would be shownas LW 4,2 .ix
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 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 20 and 21: Mean and Stand. Dev. (prestd, posts
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
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Page 38 and 39: 2 Neuron Model and Network Architec
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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
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trainbfgPurpose14trainbfgBFGS quasi
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trainbfgnet.trainParam.low_lim0.1 L
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trainbfgTo prepare a custom network
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trainbrPurpose14trainbrBayesian reg
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trainbrIf VV is not [], it must be
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trainbrThe adaptive value mu is inc
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traincTraining occurs according to
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traincgbPurpose14traincgbConjugate
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traincgbDimensions for these variab
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traincgbAlgorithmtraincgb can train
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traincgfTraining occurs according t
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traincgftraincgf(code) returns usef
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traincgfReferencesScales, L. E., In
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traincgpTraining occurs according t
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traincgptraincgp(code) returns usef
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traincgpReferencesScales, L. E., In
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traingdTraining occurs according to
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traingdaPurpose14traingdaGradient d
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traingdaValidation vectors are used
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traingdmPurpose14traingdmGradient d
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traingdmtraingdm(code) returns usef
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traingdxTraining occurs according t
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traingdx• The maximum amount of t
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trainlmTraining occurs according to
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trainlmwhere E is all errors and I
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trainossTraining occurs according t
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trainosstrainoss(code) returns usef
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trainrPurpose14trainrRandom order i
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trainr3 Set each net.layerWeights{i
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trainrpTraining occurs according to
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trainrpNetwork UseYou can create a
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trainsPurpose14trainsSequential ord
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trainsTo allow the network to adapt
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trainscgTraining occurs according t
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trainscgNetwork UseYou can create a
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tramnmxSee Alsopremnmx, prestd, pre
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trapcaAlgorithmSee AlsoPtrans = tra
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trastdSee Alsopremnmx, prepca, pres
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tribasCall sim to simulate the netw
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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
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symmetric hard-limit transfer funct
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BibliographyB
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discusses their current application
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[LiMi89] Li, J., A. N. Michel, and
Page 813 and 814:
[RuHi86b] Rumelhart, D. E., G. E. H
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Demonstrations andApplicationsC
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Tables of Demonstrations and Applic
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Tables of Demonstrations and Applic
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DSimulinkBlock Set (p. D-2)Block Ge
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Block SetEach of these blocks takes
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Block GenerationBlock GenerationThe
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Block GenerationNote that the outpu
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ECode NotesDimensions (p. E-2)Varia
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VariablesVariablesThe variables a u
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VariablesIWZWeighted inputs.Ni-by-N
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FunctionsFunctionsThe following fun
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Argument CheckingArgument CheckingT
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IndexAADALINE networkdecision bound
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IndexManhattan 8-16tuning phase 8-1
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Indexlinear transfer function 2-3,
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IndexNNT block set D-2SimulinkNNT b
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Neural Network Toolbox User's Guide

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