Multi Layer Network

Multilayer Neural Network
Presented By: Sunawar Khan
Reg No: 813/FBAS/MSCS/F14

Learning of ANN’s
Type of Neural Network
Neural Network Architecture
Basic of Neural Network
Introduction
Logistic Structure
Model Building
Development of ANN Model
Example
3

 ANN (Artificial Neural Networks) and SVM
(Support Vector Machines) are two popular
strategies for classification.
 They are well-suited for continuous-valued
inputs and outputs, unlike most
decision tree algorithms.
 Neural network algorithms are inherently
parallel; parallelization techniques can be
used to speed up the computation process.
 These factors contribute toward the
usefulness of neural networks for
classification and prediction in data mining.
5

 An Artificial Neural Network (ANN) is
an information processing paradigm
that is inspired by biological nervous
systems.
 It is composed of a large number of
highly interconnected processing
elements called neurons.
 An ANN is configured for a specific
application, such as pattern
recognition or data classification
6

 Ability to derive meaning from
complicated or imprecise data
 Extract patterns and detect trends that
are too complex to be noticed by either
humans or other computer techniques
 Adaptive learning
 Real Time Operation
7

 Conventional computers use an
algorithmic approach.
 But neural networks works similar to
human brain and learns by example.
8

9
 Some numbers…
 The human brain contains about 10 billion nerve
cells (neurons)
 Each neuron is connected to the others through
10000 synapses
 Properties of the brain
 It can learn, reorganize itself from experience
 It adapts to the environment
 It is robust and fault tolerant

10
Soma
Axon
Axon
Synapse
Synapse
Dendrites
Dendrites Soma
Two Interconnected Brain Cells (Neurons)

11
Biology Neural Network
Soma Node
Dendrites Input
Axon Output
Synapses Weight
Slow Fast
Many Neurons(109) Few Neurons(~100)

12
w1
w2
wn
x1
x2
xn
.
.
.
Y
Y1
Yn
Y2
Inputs Weights Outputs
.
.
.
Neuron (or PE)


n
i
iiWXS
1
)( Sf
Summation
Transfer
Function
bias
Artificial Neuron
)sign(y
n
0i
kii xw  
Ɵk
Composed of Basic Units and Links

13
 Processing element (PE)
 Network architecture
 Hidden layers
 Parallel processing
 Network information processing
 Inputs
 Outputs
 Connection weights
 Summation function

14
 The following are the basic
characteristics of neural network:
• Exhibit mapping capabilities, they can map
input patterns to their associated output
patterns
• Learn by examples
• Robust
• system and fault tolerant
• Process the capability to generalize. Thus,
they can predict new outcomes from past
trends

15
 An n-dimensional input vector x is mapped into variable y by means of the
scalar product and a nonlinear function mapping
 The inputs to unit are outputs from the previous layer. They are multiplied by
their corresponding weights to form a weighted sum, which is added to the
bias associated with unit. Then a nonlinear activation function is applied to it.
Ɵk
f
weighted
sum
Input
vector x
output y
Activation
function
weight
vector w

w0
w1
wn
x0
x1
xn
)sign(y
ExampleFor
n
0i
kii xw  
bias

 Several network Architecture Exists
 Feed forward backpropogation
 Recurrent
 Associative memory
 Probabilistic
 Self-organizing feature maps
 Hopfield networks
16

 In a feed forward network, information
flows in one direction along connecting
pathways, from the input layer via
hidden layers to the final output layer.
 There is not feedback, the output of any
layers of any layer does not affect that
same or preceding layer.
17

Output
x１
x2
…
xn
bias
biaswij
Input layer Hidden layers Output layer
…
… …
wjk
wkl
Transfer function is a sigmoid or any squashing function that is differentiable
1
1
Figure : Multi-layered Feed-forward neural network layout
18

 How can I design the topology of the neural
network?
 Before training can begin, the user
must decide on the network topology by
specifying the number of units in the input
layer, the number of hidden layers (if more
than one), the number of units in each
hidden layer, and the number of units in the
output layer.
19

 First decide the network topology : # of units in the
input layer, # of hidden layer(if>1), # of units in each
hidden layer, and # of units in the output layer.
 Normalizing the input values for each attribute
measured in the training tuples to [0.0-1.0]
 One input unit per domain value, each initialized to 0
 Output, if for classification and more than two
classes, one output unit per class is used.
 Once a network has been trained and its accuracy is
unacceptable, repeat the training process with a
different network topology or a different set of initial
weights
20

Number of Hidden Layers
Number of Hidden Nodes
Number of output Nodes
21

22
Output
x１
x2
…
wij
Input Layer Hidden Layers
…
… …
wjk
wkl
Output Layers

 Back Propagation described by Arthur E.
Bryson and Yu-Chi Ho in 1969, but it
wasn't until 1986, through the work of
David E. Rumelhart, Geoffrey E. Hinton
and Ronald J. Williams , that it gained
recognition, and it led to a “renaissance”
in the field of artificial neural network
research.
 The term is an abbreviation for & quot;
backwards propagation of errors & quot;.
23

 Iteratively process a set of training tuples & compare the
network's prediction with the actual known target value
 For each training tuple, the weights are modified to minimize the
mean squared error between the network's prediction and the
actual target value
 From a statistical point of view, networks perform nonlinear
regression
 Modifications are made in the “backwards” direction: from the
output layer, through each hidden layer down to the first hidden
layer, hence “backpropagation”
 Steps
 Initialize weights (to small random #s) and biases in the network
 Propagate the inputs forward (by applying activation function)
 Backpropagate the error (by updating weights and biases)
 Terminating condition (when error is very small, etc.)
24

 FEED FORWARD NETWORK activation
flows in one direction only: from the
input layer to the output layer, passing
through the hidden layer.
 Each unit in a layer is connected in the
forward direction to every unit in the next
layer.
25

 Several Nerual Network Types Is
 Multi Layer Perception
 Radial Base Function
 Kohenen Self Organizing Feature
26

 Linear Separable:
 Linear inseparable:
 Solution?
yx  yx 
yx 
27

 Back propagation is a multilayer feed forward
network with one layer of z-hidden units.
 The y output units has b(i) bias and Z-hidden
unit has b(h) as bias. It is found that both the
output and hidden units have bias. The bias acts
like weights on connection from units whose
output is always 1.
 The input layer is connected to the hidden layer
and output layer is connected to the output layer
by means of interconnection weights.
28

 The architecture of back propagation
resembles a multi-layered feed forward
network.
 The increasing the number of hidden layers
results in the computational complexity of
the network.
 As a result, the time taken for convergence
and to minimize the error may be very high.
 The bias is provided for both the hidden and
the output layer, to act upon the net input to
be calculated.
29

 The training algorithm of back propagation involves four stages.
 Initialization of weights- some small random values are
assigned.
 Feed forward- each input unit (X) receives an input signal and
transmits this signal to each of the hidden units Z 1 ,Z 2 ,……Zn
 Each hidden unit then calculates the activation function and
sends its signal Z i to each output unit. The output unit
calculates the activation function to form the response of the
given input pattern.
 Back propagation of errors- each output unit compares
activation Y k with its target value T K to determine the
associated error for that unit. Based on the error, the factor δ O
(O=1,……,m) is computed and is used to distribute the error at
output unit Y k back to all units in the previous layer. Similarly,
the factor δ H (H=1,….,p) is compared for each hidden unit H j.
 Updating of the weights and biases
30

Output nodes
Input nodes
Hidden nodes
Output vector
Input vector: xi
wij
jIj
e
O 


1
1
34
XIO ii 
ji
i
iji OwO  
Phase 1:
Propagate the Input Forward

Output nodes
Input nodes
Hidden nodes
Output vector
Input vector: xi
wij
))(1( jjjjj OTOOErr 
jk
k
kjjj wErrOOErr  )1(
35
Phase 2:
Back propagate the Error

Output nodes
Input nodes
Hidden nodes
Output vector
Input vector: xi
Oj
36
ijijij OErrlww )(
jjj Errl)(
Phase 3:
Weights/Bias Update

Output nodes
Input nodes
Hidden nodes
Output vector
Input vector: xi
wij
jIj
e
O 


1
1
))(1( jjjjj OTOOErr 
jk
k
kjjj wErrOOErr  )1(
ijijij OErrlww )(
jjj Errl)(
37
XIO ii 
ji
i
iji OwO  
Oj

38
 An n-dimensional input vector x is mapped into variable y by means of the
scalar product and a nonlinear function mapping
 The inputs to unit are outputs from the previous layer. They are multiplied by
their corresponding weights to form a weighted sum, which is added to the
bias associated with unit. Then a nonlinear activation function is applied to it.
Ɵk
f
weighted
sum
Input
vector x
output y
Activation
function
weight
vector w

w0
w1
wn
x0
x1
xn
)sign(y
ExampleFor
n
0i
kii xw  
bias

 The inputs to the network correspond to the attributes measured
for each training tuple.
 Inputs are fed simultaneously into the units making up the input
layer.
 They are then weighted and fed simultaneously to a hidden layer
 The number of hidden layers is arbitrary, although usually only one
 The weighted outputs of the last hidden layer are input to units
making up the output layer, which emits the network's prediction
 The network is feed-forward in that none of the weights cycles
back to an input unit or to an output unit of a previous layer
39

 A process by which a neural network learns
the underlying relationship between input
and outputs, or just among the inputs
 Supervised learning
 For prediction type problems
 E.g., backpropagation
 Unsupervised learning
 For clustering type problems
 Self-organizing
 E.g., adaptive resonance theory
54

Three-step process:
1. Compute temporary outputs
2. Compare outputs with
desired targets
3. Adjust the weights and
repeat the process
56

 Running Cost of Forward Back-Propagation
 Single Complete Hidden Layer
 The total running time is O(M + E) (where E is the number of
edges)
 Normally the inputs and output unit is fixed, while we
allowed to vary the number n of hidden units.
 Cost is o(n)
 Note: that this is only the cost of running forward and
backward propagation on a single example. It
is not the cost of training an entire network, which
takes multiple epochs. It is in fact possible for the
number of epochs needed to be exponential in n.
58

 Efficiency of backpropagation: each epoch (one iteration
through the training set) takes O(|D| * w), with |D| tuples
and w weights, but # of epochs can be exponential to n,
the number of inputs, in the worst case
 Network pruning
- Simplify the network structure by removing weighted
links that have the least effect on the trained network
- Then perform link, unit, or activation value clustering
 Sensitivity analysis: assess the impact that a given input
variable has on a network output.
59

60
 Weakness
 Long training time
 Require a number of parameters typically best determined
empirically, e.g., the network topology or “structure.”
 Poor interpretability: Difficult to interpret the symbolic meaning
behind the learned weights and of “hidden units” in the network
 Strength
 High tolerance to noisy data
 Ability to classify untrained patterns
 Well-suited for continuous-valued inputs and outputs
 Successful on an array of real-world data, e.g., hand-written letters
 Algorithms are inherently parallel
 Techniques have recently been developed for the extraction of rules
from trained neural networks

 In this question, I'd like to know specifically what aspects of an ANN
(specifically, a Multilayer Perceptron) might make it desirable to use over
an SVM? The reason I ask is because it's easy to answer
the opposite question: Support Vector Machines are often superior to
ANNs because they avoid two major weaknesses of ANNs:
 (1) ANNs often converge on local minima rather than global minima,
meaning that they are essentially "missing the big picture" sometimes (or
missing the forest for the trees)
 (2) ANNs often overfit if training goes on too long, meaning that for any
given pattern, an ANN might start to consider the noise as part of the
pattern.
 SVMs don't suffer from either of these two problems. However, it's not
readily apparent that SVMs are meant to be a total replacement for ANNs.
So what specific advantage(s) does an ANN have over an SVM that might
make it applicable for certain situations? I've listed specific advantages of
an SVM over an ANN, now I'd like to see a list of ANN advantages
61

 Activation function - A mathematical function applied to a node’s
activation that computes the signal strength it outputs to
subsequent nodes.
 Activation - The combined sum of a node’s incoming, weighted
signals.
 Backpropagation - A supervised learning algorithm which uses
data with associated target output to train an ANN.
 Connections - The paths signals follow between ANN nodes.
 Connection weights - Signals passing through a connection are
multiplied by that connection’s weight.
 Dataset - See Input pattern
 Epoch - One iteration through the backpropagation algorithm
(presentation of the entire training set once to the network).
 Feedforward ANN - An ANN architecture where signal flow is in
one direction only.
62

 Let wxy be the connection weight between node x, in one layer
and node y, in the following layer.
 Let ax be the net activation in node x.
 Let F(ax) be an activation function that accepts node x’s net
activation as input – the function is applied to the net activation
before node x propagates its signals onwards to the proceeding
layer. Activation functions are varied; I used one of form .
 Let be an input vector (‘network stimuli data’) that exists
in space where n equals the number of input layer nodes.
 The input layer takes its activation values from the raw input
vector element values without having the activation function
applied to them so the nth input node’s activation will be nth input
vector’s value. The activation of any non-input layer node, y, in
the network then is:
 where s is the number of nodes in the previous layer. The
signal y passes on along forward-bound connections is simply, .
Net activations in the output layer are run through the activation
function, however these nodes do not generate further forward
signals.
63

 Generalization - A well trained ANN’s ability to correctly classify unseen
input patterns by finding their similarities with training set patterns
 Input vector - See Input pattern
 Input pattern - An ANN’s input – there may be no pattern, per se. The
pattern has as many elements as the network has input layer nodes.
 Maximum training error - Criteria for deciding when to stop training an
ANN.
 Network architecture - The design of an ANN: the number of units and
their pattern of connection.
 Output - The signal a node passes on to subsequent layers (before
being multiplied by a connection weight). In the output layer, the set of
each node’s output is the ANN’s output for a particular input vector.
 Training - Process allowing an ANN to learn.
 Training set - The set of input patterns used during network training.
Each input pattern has an associated target output.
 Weights - See Connection weights.
64

Multi Layer Network

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