CONTROLO E DECISÃO INTELIGENTE 08/09

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1 CONTROLO E DECISÃO INTELIGENTE 08/09 PL #5 MatLab Neural Networks Toolbox Alexandra Moutinho Example #1 Create a feedforward backpropagation network with a hidden layer. Here is a problem consisting of inputs P and targets T that we would like to solve with a network. >> P = [ ]; >> T = [ ]; Here a network is created with one hidden layer of 5 neurons. >> net = newff(p,t,5); Here the network is simulated and its output plotted against the targets. >> Y = sim(net,p); >> plot(p,t,'rs-',p,y,'o') >> legend('t','y',0),xlabel('p') T Y Here the network is trained for 50 epochs. Again the network's output is plotted. >> net.trainparam.epochs = 50; >> net = train(net,p,t); >> Y = sim(net,p); >> figure,plot(p,t,'rs-',p,y,'o') >> legend('t','y',0),xlabel('p') P

2 T Y Type net to see the network: >> net First the architecture parameters and the subobject structures: net = Neural Network object: architecture: numinputs: 1 numlayers: 2 biasconnect: [1; 1] inputconnect: [1; 0] layerconnect: [0 0; 1 0] outputconnect: [0 1] numoutputs: 1 (read-only) numinputdelays: 0 (read-only) numlayerdelays: 0 (read-only) subobject structures: inputs: {1x1 cell} of inputs layers: {2x1 cell} of layers outputs: {1x2 cell} containing 1 output biases: {2x1 cell} containing 2 biases inputweights: {2x1 cell} containing 1 input weight layerweights: {2x2 cell} containing 1 layer weight are shown. The latter contains information about the individual objects of the network. Each layer consists of neurons with the same transfer function net.transferfcn and net input function net.netinputfcn, which are in the case of perceptrons hardlim and netsum. If neurons should have different transfer functions then they have to be arranged in different layers. The parameters net.inputweights and net.layerweights specify among other things the applied learning functions and their parameters. The next paragraph contains the training, initialization and performance functions. functions: adaptfcn: 'trains' P Controlo e Decisão Inteligente PL #5 MatLab Neural Networks Toolbox - Alexandra Moutinho 2

3 dividefcn: 'dividerand' gradientfcn: 'calcjx' initfcn: 'initlay' performfcn: 'mse' trainfcn: 'trainlm' The trainfcn and adaptfcn are used for the two different learning types, batch learning and incremental or on-line learning. By setting the trainfcn parameter you tell MatLab which training algorithm should be used, which is in our case the cyclical order incremental training/learning function trainc. The ANN toolbox includes almost 20 training functions. The performance function is the function that determines how well the ANN is doing its task. For a perceptron it is the mean absolute error performance function mae. For linear regression usually the mean squared error performance function mse is used. The initfcn is the function that initialized the weights and biases of the network. To get a list of the functions available type help nnet. To change one of these functions to another one in the toolbox or one that you have created, just assign the name of the function to the parameter, e.g. >> net.trainfcn = mytrainingfun ; The parameters that concern these functions are listed in the next paragraph. parameters: adaptparam:.passes divideparam:.trainratio,.valratio,.testratio gradientparam: (none) initparam: (none) performparam: (none) trainparam:.epochs,.goal,.max_fail,.mem_reduc,.min_grad,.mu,.mu_dec,.mu_inc,.mu_max,.show,.time By changing these parameters you can change the default behavior of the functions mentioned above. The parameters you will use the most are probably the components of trainparam. The most used of these are net.trainparam.epochs which tells the algorithm the maximum number of epochs to train, and net.trainparam.show that tells the algorithm how many epochs there should be between each presentation of the performance. Type help train for more information. The weights and biases are also stored in the network structure: weight and bias values: IW: {2x1 cell} containing 1 input weight matrix LW: {2x2 cell} containing 1 layer weight matrix b: {2x1 cell} containing 2 bias vectors other: userdata: (user information) The.IW(i,j) component is a two dimensional cell matrix that holds the weights of the connection between the input j and the network layer i. The.LW(i,j) component holds the weight matrix for the connection from the network layer j to the layer i. The cell array b contains the bias vector for each layer. Controlo e Decisão Inteligente PL #5 MatLab Neural Networks Toolbox - Alexandra Moutinho 3

4 To implement a Neural Network, 7 steps must be followed: 1. Load data source. 2. Select attributes required. 3. Decide training, validation, and testing data. 4. Data manipulations and Target generation (for supervised learning). 5. Neural Network creation (selection of network architecture) and initialization. 6. Network Training and Testing. 7. Performance evaluation. Example#2 - Iris classification with NFTOOL Load the data: >> load iris.dat >> P = iris(:,1:4); >> T = iris(:,5); Open the Neural Network Fitting Tool window with this command: >> nftool Controlo e Decisão Inteligente PL #5 MatLab Neural Networks Toolbox - Alexandra Moutinho 4

5 Load target data from workspace Load input data from workspace Data description Divide data set in subsets for training and validation Define number of hidden neurons Controlo e Decisão Inteligente PL #5 MatLab Neural Networks Toolbox - Alexandra Moutinho 5

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7 Train network Controlo e Decisão Inteligente PL #5 MatLab Neural Networks Toolbox - Alexandra Moutinho 7

8 Mean-square error Controlo e Decisão Inteligente PL #5 MatLab Neural Networks Toolbox - Alexandra Moutinho 8

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10 Compare the output with the target: >> figure,plot(t,'bo-'),hold on, plot(output,'g*-') >> legend('target','output',0) And plot the error: >> figure,plot(error) >> ylabel('error') Controlo e Decisão Inteligente PL #5 MatLab Neural Networks Toolbox - Alexandra Moutinho 10