UNIVERSITAD DE LAS AMERICAS - PUEBLA

PIERRE DERRIER # 203293

REDES NEURONALES

TAREA I

El objectivo de este tarea es de hacer la simulación de un red simple de perceptrónes feed-forward del tipo siguiente :

-> Con varios niveles escondidos

Por eso usamos MATLAB y hacemos dos simulaciones; una en cual calculamos la salida “manualmente”, es decir sin usar la libraría de redes neuronales incluida en MATLAB, y luego usamos la libraría.

%------------------------------------

% SIN LA LIBRARIA INCLUIDA EN MATLAB

%------------------------------------

%ask user to input datas

MInput = input('Enter input vector [x1 x2 x3 ... xn]:');

NbOut=input('Enter number of outputs:');

NbHidLayers=input('Enter number of hidden layers (except input and output) – Each hidden layer will contain 3 neurons:');

%generate table of number of neurons for each layers

NbLayers=NbHidLayers+2;

NbNeuronesInLayer=zeros(1,NbLayers);

NbNeuronesInLayer(1) = max(size(MInput));

NbNeuronesInLayer(NbLayers) = NbOut;

for I=2:(NbHidLayers+1),

NbNeuronesInLayer(I)=3;

end

%verbose

NbNeuronesInLayer

MaxNbNeurones=max(max(NbNeuronesInLayer))

%create weights matrice

MPoids=rand(MaxNbNeurones,NbHidLayers+1);

%prepare output matrice

MOutput=zeros(MaxNbNeurones,NbLayers);

for I=1:max(size(MInput)),

MOutput(I,1)=MInput(I);

end

%calcul of the output

for I = 2:NbLayers,

for J = 1:NbNeuronesInLayer(I),

EntreeTotale=0;

for K=1:NbNeuronesInLayer(I-1),

EntreeTotale=EntreeTotale+MOutput(K,I-1)*MPoids(K,I-1);

end

MOutput(J,I)=logsig(EntreeTotale);

end

end

%verbose

MPoids

MOutput

%------------------------------------

% CON LA LIBRARIA INCLUIDA EN MATLAB

%------------------------------------

%creacion y simulación de un red con :

%4 neurones en entrada,

%2 niveles escondidos con 3 neurones cada uno

%2 salidas

net = newff([0 1; 0 1; 0 1; 0 1],[3 3 2],{'logsig','logsig','logsig'})

input = [1;0;1;1];

output=sim(net,input)

Los resultados obtenidos son :

>> test

Enter input vector [x1 x2 x3 ... xn]:[1 0 1 1]

Enter number of outputs:2

Enter number of hidden layers (except input and output):2

NbNeuronesInLayer =

4 3 3 2

MaxNbNeurones =

4

MPoids =

0.9501 0.8913 0.8214

0.2311 0.7621 0.4447

0.6068 0.4565 0.6154

0.4860 0.0185 0.7919

MOutput =

( entrada – niveles escondidos …- salida)

1.0000 0.8852 0.8662 0.8361

0 0.8852 0.8662 0.8361

1.0000 0.8852 0.8662 0

1.0000 0 0 0

(Luego, con la libraría incluida en MATLAB)

net =

Neural Network object:

architecture:

numInputs: 1

numLayers: 3

biasConnect: [1; 1; 1]

inputConnect: [1; 0; 0]

layerConnect: [0 0 0; 1 0 0; 0 1 0]

outputConnect: [0 0 1]

targetConnect: [0 0 1]

numOutputs: 1 (read-only)

numTargets: 1 (read-only)

numInputDelays: 0 (read-only)

numLayerDelays: 0 (read-only)

subobject structures:

inputs: {1x1 cell} of inputs

layers: {3x1 cell} of layers

outputs: {1x3 cell} containing 1 output

targets: {1x3 cell} containing 1 target

biases: {3x1 cell} containing 3 biases

inputWeights: {3x1 cell} containing 1 input weight

layerWeights: {3x3 cell} containing 2 layer weights

functions:

adaptFcn: 'trains'

initFcn: 'initlay'

performFcn: 'mse'

trainFcn: 'trainlm'

parameters:

adaptParam: .passes

initParam: (none)

performParam: (none)

trainParam: .epochs, .goal, .max_fail, .mem_reduc,

.min_grad, .mu, .mu_dec, .mu_inc,

.mu_max, .show, .time

weight and bias values:

IW: {3x1 cell} containing 1 input weight matrix

LW: {3x3 cell} containing 2 layer weight matrices

b: {3x1 cell} containing 3 bias vectors

other:

userdata: (user stuff)

output =

0.5678

0.0228