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Neural Networks

Neural Networks. John Riebe and Adam Profitt. What is a neuron?. P R Elements of the input vector W Weights ∑ Summer b Bias n Sum of all P elements and b ƒ Translation Function a Output. Weights: Weights are scalars that multiply each input element

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Neural Networks

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  1. Neural Networks John Riebe and Adam Profitt

  2. What is a neuron? PR Elements of the input vector W Weights ∑ Summer b Bias n Sum of all P elements and b ƒ Translation Function a Output Weights: Weights are scalars that multiply each input element Summer: The summer sums the input elements, PR, together with the bias Bias: A bias is a number that is added to the total from the summer Translation Function: A translation function is one of many specific functions used in neural networking.

  3. Layers of the Neural Network • There are only three different types of layers in a network: • The Input Layer • Moves the input vectors into each neuron of the first hidden layer • The Hidden Layers • Performs the bulk of the computations in most networks • Hidden layers are not always required • The Output Layer • Each neuron in the output layer outputs it’s own result

  4. Translation Functions

  5. Types of Neural Networks • Perceptrons: • Used to classify data. • Applies the hard-limit transfer function. • Usually does not have any hidden layers. • Linear Filters • Used to solve linearly separable problems. • Applies the linear transfer function. • Backpropagation • Generally has only one hidden layer. • Can solve any reasonable problem. • Hidden layers use sigmoid translations, outputs use the linear transfer function

  6. Training Neurons Training a network sets the biases and weights in each neuron • To train a network you need: • A network • An input • A target vector • There are many different types of • training algorithms. To name a few: • Levenberg-Marquardt • BFGS quasi-Newton • Bayesian regularization • One step secant • Random order incremental • Training algorithms • Gives a network an input • Receives the output • Calculates error between output and target • Adjusts weights and biases • Goes back to step 1 Each time the algorithm goes through the steps is called an epoch. Most networks go through many epochs.

  7. MatlabApplication

  8. The newff Function • Create a feed-forward network • Syntax • net = newff • net = newff(PR,[S1 S2...Si],{TF1 TF2...TFi}) • Description • net = newff creates a new network with a dialog box. • newff(PR,[S1 S2...Si],{TF1 TF2...TFi}) takes, • PR - R x 2 matrix of min and max values for R input elements. • Si - Size of ith layer, for Nl layers. • TFi - Transfer function of ith layer, default = 'tansig'.

  9. The train Function Trains a neural network Syntax net = train(net,P,T) Description train trains a network. train(net,P,T) takes, net - Neural network object. P - Network inputs. T - Network targets, default = zeros.

  10. The sim Function The sim function simulates a neural network. This function feeds the network the input, P, and displays the results. Syntaxsim(net,P) Descriptionsim simulates neural networks. sim(net,P) takes, net - Network. P - Network inputs.

  11. Transfer Functions Revisited • Transfer functions: • Hard-Limit • a = hardlim(n) Outputs either a 1 or a 0 • Linear • a = purelin(n) Outputs the scaled and summed input • Log-Sigmoid • a = logsig(n) Squeezes the input to between 0 and 1 • Tan-Sigmoid • a = tansig(n) Squeezes the input to between -1 and 1

  12. The Baum-Haussler Rule The Baum-Haussler Rule is one of the most useful rules for neural networks. Nhidden≤ (Ntrain • Etolerance) / (Npts + Noutputs) This rule helps you determine the maximum number of neurons you will need for your network to function properly. This is NOT a law: it will not work in all situations. Sometimes you just have to use another method.

  13. Bibliography Demuth, Howard and Mark Beale. “Neural Network Toolbox User’s Guide.“ 1992-2003 URL: http://www.mathworks.com/access/helpdesk/help/toolbox/nnet/nnet.shtml

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