NNFL 3 - Guru Nanak Dev Engineering College

CHAPTER 3
SUPERVISED
LEARNING NETWORK
“Principles of Soft Computing, 2nd
Edition”
by S.N. Sivanandam & SN Deepa
Copyright © 2011 Wiley India Pvt. Ltd. All rights reserved.

DEFINITION OF SUPERVISED LEARNING
NETWORKS
 Training and test data sets
 Training set; input & target are specified
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PERCEPTRON NETWORKS
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 Linear threshold unit (LTU)
Σ
x1
x2
xn
..
.
w1
w2
wn
w0
Σ wi xi
1 if Σ wi xi >0
f(xi)=
-1 otherwise
o
{
n
i=0
i=0
n
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PERCEPTRON LEARNING
wi = wi + ∆wi
∆wi = η (t - o) xi
where
t = c(x) is the target value,
o is the perceptron output,
η Is a small constant (e.g., 0.1) called learning rate.
 If the output is correct (t = o) the weights wi are not changed
 If the output is incorrect (t ≠ o) the weights wi are changed such
that the output of the perceptron for the new weights is closer to t.
 The algorithm converges to the correct classification
• if the training data is linearly separable
∀ η is sufficiently small
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LEARNING ALGORITHM
 Epoch : Presentation of the entire training set to the neural
network.
 In the case of the AND function, an epoch consists of four sets of
inputs being presented to the network (i.e. [0,0], [0,1], [1,0], [1,1]).
 Error: The error value is the amount by which the value output by
the network differs from the target value. For example, if we
required the network to output 0 and it outputs 1, then Error = -1.
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 Target Value, T : When we are training a network we not only
present it with the input but also with a value that we require the
network to produce. For example, if we present the network with
[1,1] for the AND function, the training value will be 1.
 Output , O : The output value from the neuron.
 Ij : Inputs being presented to the neuron.
 Wj : Weight from input neuron (Ij) to the output neuron.
 LR : The learning rate. This dictates how quickly the network
converges. It is set by a matter of experimentation. It is typically
0.1.
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TRAINING ALGORITHM
 Adjust neural network weights to map inputs to outputs.
 Use a set of sample patterns where the desired output (given the
inputs presented) is known.
 The purpose is to learn to
• Recognize features which are common to good and bad
exemplars
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MULTILAYER PERCEPTRON
Output Values
Input Signals (External Stimuli)
Output Layer
Adjustable
Weights
Input Layer
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LAYERS IN NEURAL NETWORK
 The input layer:
• Introduces input values into the network.
• No activation function or other processing.
 The hidden layer(s):
• Performs classification of features.
• Two hidden layers are sufficient to solve any problem.
• Features imply more layers may be better.
 The output layer:
• Functionally is just like the hidden layers.
• Outputs are passed on to the world outside the neural network.
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ADAPTIVE LINEAR NEURON (ADALINE)
In 1959, Bernard Widrow and Marcian Hoff of Stanford developed
models they called ADALINE (Adaptive Linear Neuron) and MADALINE
(Multilayer ADALINE). These models were named for their use of
Multiple ADAptive LINear Elements. MADALINE was the first neural
network to be applied to a real world problem. It is an adaptive filter
which eliminates echoes on phone lines.
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ADALINE MODEL
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ADALINE LEARNING RULE
Adaline network uses Delta Learning Rule. This rule is also called as
Widrow Learning Rule or Least Mean Square Rule. The delta rule for
adjusting the weights is given as (i = 1 to n):
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 Initialize
• Assign random weights to all links
 Training
• Feed-in known inputs in random sequence
• Simulate the network
• Compute error between the input and the
output (Error Function)
• Adjust weights (Learning Function)
• Repeat until total error < ε
 Thinking
• Simulate the network
• Network will respond to any input
• Does not guarantee a correct solution even
for trained inputs
USING ADALINE NETWORKS
Initialize
Training
Thinking
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MADALINE NETWORK
MADALINE is a Multilayer Adaptive Linear Element. MADALINE was the
first neural network to be applied to a real world problem. It is used in
several adaptive filtering process.
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BACK PROPAGATION NETWORK
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 A training procedure which allows multilayer feed forward Neural
Networks to be trained.
 Can theoretically perform “any” input-output mapping.
 Can learn to solve linearly inseparable problems.
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MULTILAYER FEEDFORWARD
NETWORK
Inputs
Hiddens
Outputs
I1
I2
I3
I0
h0
h1
h2
o0
o1
Inputs
Hiddens
Outputs
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MULTILAYER FEEDFORWARD NETWORK:
ACTIVATION AND TRAINING
 For feed forward networks:
• A continuous function can be
• differentiated allowing
• gradient-descent.
• Back propagation is an example of a gradient-descent
technique.
• Uses sigmoid (binary or bipolar) activation function.
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In multilayer networks, the activation function is
usually more complex than just a threshold function,
like 1/[1+exp(-x)] or even 2/[1+exp(-x)] – 1 to allow for
inhibition, etc.
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 Gradient-Descent(training_examples, η)
 Each training example is a pair of the form <(x1,…xn),t> where (x1,
…,xn) is the vector of input values, and t is the target output value,
η is the learning rate (e.g. 0.1)
 Initialize each wi to some small random value
 Until the termination condition is met, Do
• Initialize each ∆wi to zero
• For each <(x1,…xn),t> in training_examples Do
GRADIENT DESCENT
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Input the instance (x1,…,xn) to the linear unit and compute
the output o
For each linear unit weight wi Do
• ∆wi= ∆wi + η (t-o) xi
• For each linear unit weight wi Do
• wi=wi+∆wi
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 Batch mode : gradient descent
w=w - η ∇ED[w] over the entire data D
ED[w]=1/2Σd(td-od)2
 Incremental mode: gradient descent
w=w - η ∇Ed[w] over individual training examples d
Ed[w]=1/2 (td-od)2
 Incremental Gradient Descent can approximate Batch Gradient
Descent arbitrarily closely if η is small enough.
MODES OF GRADIENT DESCENT
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SIGMOID ACTIVATION FUNCTION
Σ
x1
x2
xn
..
.
w1
w2
wn
w0
x0=1
net=Σi=0
n
wi xi
o
o=σ(net)=1/(1+e-net
)
σ(x) is the sigmoid function: 1/(1+e-x)
dσ(x)/dx= σ(x) (1- σ(x))
Derive gradient decent rules to train:
• one sigmoid function
∂E/∂wi = -Σd(td-od) od (1-od) xi
• Multilayer networks of sigmoid units
backpropagation
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 Initialize each wi to some small random value.
 Until the termination condition is met, Do
• For each training example <(x1,…xn),t> Do
• Input the instance (x1,…,xn) to the network and compute the
network outputs ok
• For each output unit k
– δk=ok(1-ok)(tk-ok)
• For each hidden unit h
– δh=oh(1-oh) Σk wh,k δk
• For each network weight w,j Do
• wi,j=wi,j+∆wi,j where
– ∆wi,j= η δj xi,j
BACKPROPAGATION TRAINING
ALGORITHM
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 Gradient descent over entire network weight vector
 Easily generalized to arbitrary directed graphs
 Will find a local, not necessarily global error minimum -in practice often
works well (can be invoked multiple times with different initial weights)
 Often include weight momentum term
∆wi,j(t)= η δj xi,j + α ∆wi,j (t-1)
 Minimizes error training examples
 Will it generalize well to unseen instances (over-fitting)?
 Training can be slow typical 1000-10000 iterations (use Levenberg-
Marquardt instead of gradient descent)
BACKPROPAGATION
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APPLICATIONS OF BACKPROPAGATION
NETWORK
 Load forecasting problems in power systems.
 Image processing.
 Fault diagnosis and fault detection.
 Gesture recognition, speech recognition.
 Signature verification.
 Bioinformatics.
 Structural engineering design (civil).
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RADIAL BASIS FUCNTION NETWORK
 The radial basis function (RBF) is a classification and functional
approximation neural network developed by M.J.D. Powell.
 The network uses the most common nonlinearities such as
sigmoidal and Gaussian kernel functions.
 The Gaussian functions are also used in regularization networks.
 The Gaussian function is generally defined as
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RADIAL BASIS FUCNTION NETWORK
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SUMMARY
This chapter discussed on the several supervised learning networks
like
 Perceptron,
 Adaline,
 Madaline,
 Backpropagation Network,
 Radial Basis Function Network.
Apart from these mentioned above, there are several other supervised
neural networks like tree neural networks, wavelet neural network,
functional link neural network and so on.
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NNFL 3 - Guru Nanak Dev Engineering College

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