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Neural Networks John Riebe and Adam Profitt What is a neuron? Layers of the Neural Network Translation Functions Types of Neural Networks Training Neurons Matlab ... – PowerPoint PPT presentation

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Title: Neural%20Networks

Neural Networks
John Riebe and Adam Profitt
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.
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
  • Hidden layers are not always required
  • The Output Layer
  • Each neuron in the output layer outputs its own

Translation Functions
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

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
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
  • 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

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.
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.
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
The Baum-Haussler Rule
The Baum-Haussler Rule is one of the most useful
rules for neural networks.
Nhidden (Ntrain Etolerance) / (Npts
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.
Demuth, Howard and Mark Beale. Neural Network
Toolbox Users Guide. 1992-2003 URL
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