Artificial Neural Network (Back-Propagation Neural Network)

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Artificial Neural Network (Back-Propagation Neural Network). Yusuf Hendrawan , STP., M.App.Life Sc., Ph.D. http://research.yale.edu/ysm/images/78.2/articles-neural-neuron.jpg. http://faculty.washington.edu/chudler/color/pic1an.gif. Neurons. Biologica l. Artificial. A typical AI agent. - PowerPoint PPT Presentation

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Artificial Neural Network (Back-Propagation Neural Network)

Artificial Neural Network(Back-Propagation Neural Network)Yusuf Hendrawan, STP., M.App.Life Sc., Ph.D

Neurons

http://faculty.washington.edu/chudler/color/pic1an.gif

http://research.yale.edu/ysm/images/78.2/articles-neural-neuron.jpgBiologicalArtificial

A typical AI agentNeural Network LayersEach layer receives its inputs from the previous layer and forwards its outputs to the next layer

http://smig.usgs.gov/SMIG/features_0902/tualatin_ann.fig3.gifMultilayer feed forward networkIt contains one or more hidden layers (hidden neurons).Hidden refers to the part of the neural network is not seen directly from either input or output of the network . The function of hidden neuron is to intervene between input and output.By adding one or more hidden layers, the network is able to extract higher-order statistics from input

Neural Network LearningBack-Propagation Algorithm:function BACK-PROP-LEARNING(examples, network) returns a neural network inputs: examples, a set of examples, each with input vector x and output vector y network, a multilayer network with L layers, weights Wj,i , activation function g

repeat for each e in examples do for each node j in the input layer do aj xj[e] for l = 2 to M do ini j Wj,i aj ai g(ini) for each node i in the output layer do Dj g(inj) i Wji Di

for l = M 1 to 1 do for each node j in layer l do Dj g(inj) i Wj,i Di for each node i in layer l + 1 do Wj,i Wj,i + a x aj x Di until some stopping criterion is satisfied return NEURAL-NET-HYPOTHESIS(network)

[Russell, Norvig] Fig. 20.25 Pg. 746Back-Propagation Illustration

ARTIFICIAL NEURAL NETWORKS Colin Fahey's Guide (Book CD)X1X2YVoWoZ1Z2Z3Z4Input (X)HiddenOutput (Y)X1X20.30.40.50.60.20.30.40.7Input (X)Output / Target (T)T0.10.80.40.5Jumlah Neuron pada Input Layer2Jumlah Neuron pada Hidden Layer4Jumlah Neuron pada Output Layer1Learning rate ()0.1Momentum (m)0.9Target Error0.01Maximum Iteration1000Bobot Awal Input ke HiddenV11 = 0.75V21 = 0.35V12 = 0.54V22 = 0.64V13 = 0.44V23 = 0.05V14 = 0.32V24 = 0.81Bias ke HiddenVo11 = 0.07Vo21 = 0.12Vo12 = 0.91Vo22 = 0.23Vo13 = 0.45Vo23 = 0.85Vo14 = 0.25Vo24 = 0.09Bobot Awal Hidden ke OutputW1 = 0.04W2 = 0.95W3 = 0.33W4 = 0.17Bias ke OutputWo1 = 0.66Wo2 = 0.56Wo3 = 0.73Wo4 = 0.01Menghitung Zin & Z dari input ke hiddenZin(1) = (X1 * V11) + (X2 * V21) = (0.3 * 0.75) + (0.4 * 0.35) = 0.302Zin(2) = (X1 * V12) + (X2 * V22) = (0.3 * 0.54) + (0.4 * 0.64) = 0.418Zin(3) = (X1 * V13) + (X2 * V23) = (0.3 * 0.44) + (0.4 * 0.05) = 0.152Zin(4) = (X1 * V14) + (X2 * V24) = (0.3 * 0.32) + (0.4 * 0.81) = 0.42

Menghitung Yin & Y dari hidden ke outputYin = (Z(1) * W1) + (Z(2) * W2) + (Z(3) * W3) + (Z(4) * W4)= (0.57 * 0.04) + (0.603 * 0.95) + (0.538 * 0.33) + (0.603 * 0.17)= 0.876

Menghitung dev antara Y dengan output nyatadev = (T - Y) * Y * (1 - Y) = (0.1 0.706) * 0.706 * (1 0.706) = -0.126Menghitung selisihselisih = T - Y= -0.606Back-Propagation

Menghitung din dari output ke hiddendin(1) = (dev * W1) = (-0.126 * 0.04) = -0.00504din(2) = (dev * W2) = (-0.126 * 0.95) = -0.1197din(3) = (dev * W3) = (-0.126 * 0.33) = -0.04158din(4) = (dev * W4) = (-0.126 * 0.17) = -0.02142Menghitung dd (1) = (din(1) * Z(1) * (1 - Z(1) ) = (-0.00504 * 0.575 * (1 0.575) = -0.00123d (2) = (din(2) * Z(2) * (1 - Z(2) ) = (-0.1197 * 0.603 * (1 0.603) = -0.02865d (3) = (din(3) * Z(3) * (1 - Z(3) ) = (-0.04158 * 0.538 * (1 0.538) = -0.01033d (4) = (din(4) * Z(4) * (1 - Z(4) ) = (-0.02142 * 0.603 * (1 0.603) = -0.00512Mengkoreksi bobot (W) dan bias (Wo)W1 = W1 + ( * dev * Z(1) ) + (m * Wo(1)) = 0.04 + (0.1 * -0.126 * 0.575) + (0.9 * 0.66) = 0.627 W2 = W2 + ( * dev * Z(2) ) + (m * Wo(2)) = 0.95 + (0.1 * -0.126 * 0.603) + (0.9 * 0.56) = 1.45 W3 = W3 + ( * dev * Z(3) ) + (m * Wo(3)) = 0.33 + (0.1 * -0.126 * 0.538) + (0.9 * 0.73) = 0.98 W4 = W4 + ( * dev * Z(4) ) + (m * Wo(4)) = 0.17 + (0.1 * -0.126 * 0.603) + (0.9 * 0.01) = 0.171 Wo1 = ( * Z(1) ) + (m * Wo(1)) = (0.1 * 0.575) + (0.9 * 0.66) = 0.65 Wo2 = ( * Z(2) ) + (m * Wo(2)) = (0.1 * 0.603) + (0.9 * 0.56) = 0.564 Wo3 = ( * Z(3) ) + (m * Wo(3)) = (0.1 * 0.538) + (0.9 * 0.73) = 0.71 Wo4 = ( * Z(4) ) + (m * Wo(4)) = (0.1 * 0.603) + (0.9 * 0.01) = 0.0693 Mengkoreksi bobot (V) dan bias (Vo)V11 = V11 + ( * d (1) * X1 ) + (m * Vo(11)) = 0.75 + (0.1 * -0.00123 * 0.3) + (0.9 * 0.07) = 0.8129 V12 = V12 + ( * d (2) * X1 ) + (m * Vo(12)) = 0.54 + (0.1 * -0.02865 * 0.3) + (0.9 * 0.91) = 1.3581V13 = V13 + ( * d (3) * X1 ) + (m * Vo(13)) = 0.44 + (0.1 * -0.01033 * 0.3) + (0.9 * 0.45) = 0.8446 V14 = V14 + ( * d (4) * X1 ) + (m * Vo(14)) = 0.32 + (0.1 * -0.00512 * 0.3) + (0.9 * 0.25) = 0.5448 V21 = V21 + ( * d (1) * X2 ) + (m * Vo(21)) = 0.35 + (0.1 * -0.00123 * 0.4) + (0.9 * 0.12) = 0.4579 V22 = V22 + ( * d (2) * X2 ) + (m * Vo(22)) = 0.64 + (0.1 * -0.02865 * 0.4) + (0.9 * 0.23) = 0.8458 V23 = V23 + ( * d (3) * X2 ) + (m * Vo(23)) = 0.05 + (0.1 * -0.01033 * 0.4) + (0.9 * 0.85) = 0.8145 V24 = V24 + ( * d (4) * X2 ) + (m * Vo(24)) = 0.81 + (0.1 * -0.00512 * 0.4) + (0.9 * 0.09) = 0.8907 Mengkoreksi bobot (V) dan bias (Vo)Vo11 = ( * d (1) * X1 ) + (m * Vo11) = (0.1 * -0.00123*0.3)+(0.9*0.07) = 0.0629Vo12 = ( * d (2) * X1 ) + (m * Vo12) = (0.1 * -0.02865*0.3)+(0.9*0.91) = 0.8181Vo13 = ( * d (3) * X1 ) + (m * Vo13) = (0.1 * -0.01033*0.3)+(0.9*0.45) = 0.4046Vo14 = ( * d (4) * X1 ) + (m * Vo14) = (0.1 * -0.00512*0.3)+(0.9*0.25) = 0.2248Vo21 = ( * d (1) * X2 ) + (m * Vo21) = (0.1 * -0.00123*0.4)+(0.9*0.12) = 0.1079Vo22 = ( * d (2) * X2 ) + (m * Vo22) = (0.1 * -0.02865*0.4)+(0.9*0.23) = 0.2058Vo23 = ( * d (3) * X2 ) + (m * Vo23) = (0.1 * -0.01033*0.4)+(0.9*0.85) = 0.7645Vo24 = ( * d (4) * X2 ) + (m * Vo24) = (0.1 * -0.00512*0.4)+(0.9*0.09) = 0.0807

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