SoftComputingUNIT-1_Neural_Network_Architectures.pptx

UNIT- 1
Neural Network Architectures: Supervised Learning:
Backpropagation Network architecture, Backpropagation
algorithm, Limitation, Characteristics and Application of
EBPA, Bidirectional associative memories (BAM),
Unsupervised Learning: Hebbian Learning, Generalized
Hebbian learning algorithm, Competitive learning, Self-
Organizing Computational Maps: Kohonen Network,
Applications of ANN to solve real world’s problems.

CONCEPT OF COMPUTING SYSTEMS
Computer is an electronic device that takes raw data
as input from the user and processes these data
under the control of set of instructions (called
program) and gives the result (output) and saves
output for the future use.

COMPUTER SYSTEM
 Data is a collection of unorganized facts & figures
and does not provide any further information
regarding patterns, context, etc. Hence data means
"unstructured facts and figures".
 Information is a structured data i.e. organized
meaningful and processed data. To process the
data and convert into information, a computer is
used.

COMPONENTS OF COMPUTER
1. Hardware
2. Software
3. Data
4. User

HARDWARE
 The term hardware
refers to mechanical
device that makes up
computer. Computer
hardware consists of
interconnected
electronic devices that
we can use to control
computer’s operation,
input and output.
Examples of hardware
are CPU, keyboard,
mouse, hard disk, etc.

SOFTWARE
 A set of instructions that drives computer to do
stipulated tasks is called a program. Software can
be categorized into two types −
 System software
Application software

DATA
 Data is a collection of unorganized facts & figures
and does not provide any further information
regarding patterns, context, etc. Hence data means
"unstructured facts and figures".

FUNCTIONS OF COMPUTER
 Receiving Input: Data is fed into computer through
various input devices like keyboard, mouse, digital pens,
etc. Input can also be fed through devices like CD-ROM,
pen drive, scanner, etc.
 Processing the information:- Operations on the input
data are carried out based on the instructions provided
in the programs.
 Storing the information:- After processing, the
information gets stored in the primary or secondary
storage area.
 Producing output:- The processed information and other
details are communicated to the outside world through
output devices like monitor, printer, etc.

CHARACTERISTICS OF THE COMPUTER
SYSTEM

BASIC APPLICATIONS OF COMPUTER
 Medical Field
 Entertainment
 Industry
 Education
 Government
 Banking
 Business
 Training
 Arts
 Science and Engineering

DATA PROCESSING AND ITS STEPS
 Data processing is a process of converting raw
facts or data into a meaningful information.

STAGES OF DATA PROCESSING
 Collection:- Collection of data refers to gathering of
data. The data gathered should be defined and
accurate.
 Preparation:- Preparation is a process of
constructing a dataset of data from different
sources for future use in processing step of cycle.
 Input:- Input refers to supply of data for processing.
It can be fed into computer through any of input
devices like keyboard, scanner, mouse, etc.

STAGES OF DATA PROCESSING
 Processing:- The process refers to concept of an
actual execution of instructions. In this stage, raw
facts or data is converted to meaningful information.
 Output and Interpretation:- In this process, output
will be displayed to user in form of text, audio,
video, etc. Interpretation of output provides
meaningful information to user.
 Storage:- In this process, we can store data,
instruction and information in permanent memory
for future reference.

INTRODUCTION TO SOFT COMPUTING

COMPUTING MEANING
The process or act of
calculation
C=a+b

COMPUTING DEFINITION
1. The procedure of calculating; determining something
by mathematical or logical methods
2. The process of accomplishing a particular task with the
help of a computer or a computing device is known as
computing. It should provide precise and accurate
solutions, also it makes easy to find the mathematical
solution of the problems.
3. "In a general way, we can define computing to mean
any goal-oriented activity requiring, benefiting from, or
creating computers.‖ This is a very broad definition
that comprises the development of computer
hardware, the use of computer applications, and the
development of computer software.

CONCEPT OF COMPUTING :
EXAMPLE:-
According to the concept of computing, the input is
called an antecedent and the output is called the
consequent. For example, Adding information in
DataBase, Compute the sum of two numbers using a
C program, etc.

TYPES OF COMPUTING
1. HARD COMPUTING
2. SOFT COMPUTING
3. HYBRID COMPUTING

HARD COMPUTING
It is a traditional approach used in computing which
needs an accurately stated analytical model proposed
by Dr. Lotfi Zadeh.
 Example of Hard computing
a) Solving numerical problems (eg. Roots of
polynomial)
b) Searching & sorting techniques
c) Solving computational geometry problems (eg.
Shortest tour in graph, finding closest pair of points
given a set of points etc.)

CHARACTERISTICS OF HARD COMPUTING
 The precise result is guaranteed.
 The control action is unambiguous.
 The control action is formally defined (i.e. with a
mathematical model)

PROS AND CONS OF HARD COMP.
Advantages
 Accurate solutions can be obtained
 Faster
Disadvantages
 Not suitable for real world problems
 Cannot handle imprecision and partial truth

Now, the question arises
that if we have hard
computing then why do
we require the need for
soft computing.

TAKE A EXAMPLE:
Consider a problem where a string
w1 is “abc” and string w2 is “abd”.
Problem-1 :
Tell that whether w1 is the same as w2 or not?
Solution –
The answer is simply No, it means there is an
algorithm by which we can analyze it.

TAKE A EXAMPLE:
 Problem-2 :
Tell how much these two strings are similar?
 Solution –
The answer from conventional computing is either
YES or NO. But these maybe 80% similar, this can
be answered only by Soft Computing.

NEED FOR SOFT COMPUTING :
 Many analytical models are valid for ideal cases. Real-
world problems exist in a non-ideal environment.
 Soft computing provides insights into real-world problems
and is just not limited to theory.

NEED FOR SOFT COMPUTING :
 Hard computing is best suited for solving mathematical
problems which give some precise answers.
 Some important fields like Biology, Medicine and
humanities, etc are still intractable using Convention
mathematical and Analytical models.
 It is possible to map the human mind with the help of Soft
computing but it is not possible with Convention
mathematical and Analytical models.

SOFT COMPUTING
The term soft computing was proposed by the
inventor of fuzzy logic, Lotfi A. Zadeh
“Soft computing is a collection of methodology that
aim to exploit the tolerance of imprecision &
uncertainty to achieve tractability, robustness, & low
solution on cost. Its principal constituents are fuzzy
logic, neuro- Computing & probabilistic reasoning.
The role model for soft computing is human mind”
The objective of soft computing is to provide precise
approximation and quick solutions for complex real-
life problems.

EXAMPLE OF SOFT COMPUTING
 Hand written character recognition (A.I.)
 Money allocation problem (Evolutionary Computing)
 Robot movement (Fuzzy logic)

CHARACTERISTICS OF SOFT COMPUTING
 It may not yield a precise solution.
 Algorithms are adaptive.
 In soft computing, you can consider an example
where you can see the evolution changes for a
specific species like the human nervous system
and behavior of an Ant’s, etc.
 Learning from experimental data.

RECENT DEVELOPMENT IN SOFT COMPUTING
:
1. In the field of Big Data, soft computing working for data
analyzing models, data behavior models, data decision, etc.
2. In case of Recommender system, soft computing plays an
important role for analyzing the problem on the based of
algorithm and works for precise results.
3. In Behavior and decision science, soft computing used in
this for analyzing the behavior, and model of soft computing
works accordingly.
4. In the fields of Mechanical Engineering, soft computing is a
role model for computing problems such that how a machine
will works and how it will make the decision for a specific
problem or input given.
5. In this field of Computer Engineering, you can say it is core
part of soft computing and computing working on advanced
level like Machine learning, Artificial intelligence, etc.

SOFT COMPUTING VS. HARD COMPUTING

How to do Soft Computing
How students learn from his teacher?
 Teacher asks questions & till the answers then.
 Teacher puts questions & hints answer & ask
whether the answers are correct or not
 Students thus learn a topic & solve in his memory.
 Based on the knowledge he solves new problems.
 This is the way how human brain works.
 Based on this concept Artificial neural N/W is used
to solve problems.

 How world selects the best?
 It starts with a population (Random).
 Reproduces another population (Next generation).
 Rank the population & select the superior
individuals.
 Genetic algorithm is based on these natural
phenomena.

How Doctor treats his patient?
 Doctor asks the patient about suffering.
 Doctor finds the symptoms of diseases.
 Doctor prescribed test & medicines.
 Symptoms are correlated with diseases with
uncertainty.
 Doctor prescribes tests/medicines fuzzily.

SOFT COMPUTING DEVELOPMENT HISTORY
Soft = Evolutionary + Neural + Fuzzy
Computing Computing Networks Logic
Zadeh Rechenberg Mcculloch Zadeh
1981 1960 1943 1965
Evolutionary = Genetic + Evolution + Evolutionary + Genetic
Computing Programming Strategies Programming Algorithms
Rechenberg Koza Rechenberg Fogel I Iolland
1960 1992 1965 1962 1970

APPROXIMATE REASONING
x = S1A′s are B′s
y = S2C′s are D′s
------------------------
z = S3E′s are F′s

NEURAL NETWORK
 Neural networks were developed in the 1950s,
which helped soft computing to solve real-world
problems, which a computer cannot do itself.
 An artificial neural network (ANN) emulates a
network of neurons that makes a human brain
(means a machine that can think like a human
mind). Thereby the computer or a machine can
learn things so that they can take decisions like the
human brain.

FUZZY LOGIC
 Fuzzy logic is nothing but mathematical logic which
tries to solve problems with an open and imprecise
spectrum of data. It makes it easy to obtain an
array of precise conclusions.

GENETIC ALGORITHM
 The genetic algorithm was introduced by Prof. John
Holland in 1965. It is used to solve problems based
on principles of natural selection, that come under
evolutionary algorithm. They are usually used for
optimization problems like maximization and
minimization of objective functions, which are of two
types of an ant colony and swarm particle. It follows
biological processes like genetics and evolution.

UNIT- 1
Concept of Computing Systems, Introduction to Soft
Computing, Soft Computing vs. Hard Computing,
Components of Soft Computing, Neural Networks:
Structure and function of Biological Neuron and
Artificial Neuron, Definition and characteristics of ANN,
Training techniques in different ANNs, Activation
functions,
Different ANNs architectures, Introduction to basic ANN
architectures: McCulloch & Pitts model, Perceptron Model,
Linear separability, ADALINE and MADALINE.

INTRODUCTION TO NEURAL NETWORK

BIOLOGICAL INSPIRATIONS
Humans perform complex tasks like vision,
motor control, or language understanding very
well.
One way to build intelligent machines is to try to
imitate the (organizational principles of) human
brain.

HUMAN BRAIN
• The brain is a highly complex, non-linear, and parallel computer, composed of
some 1011 neurons that are densely connected (~104 connection per neuron).
We have just begun to understand how the brain works...
• A neuron is much slower (10-3sec) compared to a silicon logic gate (10-9sec),
however the massive interconnection between neurons make up for
the comparably slow rate.
– Complex perceptual decisions are arrived at quickly (within a few hundred
milliseconds)
• 100-Steps rule: Since individual neurons operate in a few milliseconds,
calculations do not involve more than about 100 serial steps and the
information sent from one neuron to another is very small (a few bits)
• Plasticity: Some of the neural structure of the brain is present at birth, while
other parts are developed through learning, especially in early stages of life, to
adapt to the environment (new inputs).

BIOLOGICAL NEURON
A variety of different neurons exist with different branching
structures.
The connections of the network and the strengths of the
individual synapses establish the function of the network.

BIOLOGICAL NEURON/HUMAN BRAIN
 Human brain contains about 1010 or 1011 basic units called
“Neurons”. Each neuron in turn ,is connected to about 104
other neurons.
 Size of brain is around 1.5 kg.
 Size of Avg. neuron is around 1.5 * 10-9 grams.

BIOLOGICAL NEURON STRUCTURE
SOMA
SYNAPSE

WORKING OF A BIOLOGICAL NEURON
A typical neuron consists of the following four parts with the help of
which we can explain its working
 Dendrites − They are tree-like branches, responsible for
receiving the information from other neurons it is connected to. In
other sense, we can say that they are like the ears of neuron.
The dendrites behave as input channel.
 Soma − It is the cell body of the neuron and is responsible for
processing of information, they have received from dendrites.
 Axon − Axon is electrically active and serves as an output
channel. It is just like a cable through which neurons send the
information.
 Synapses − The axon terminates in a specialized contact called
synapse or synaptic junction that connects the axon with the
dendrites links of another neuron. It contains a neuro-transmitter
fluid which is responsible for accelerating or retarding the electric
charges to soma.

ARTIFICIAL NEURAL NETWORKS
Computational models inspired by the human brain:
– Massively parallel, distributed system, made up
of simple processing units (neurons)
– Synaptic connection strengths among neurons are
used to store the acquired knowledge.
– Knowledge is acquired by the network
from its environment through a learning
process

BIOLOGICAL AND ARTIFICIAL NEURON

SIMPLE MODEL OF AN ARTIFICIAL
NEURON
Biological Neural Network (BNN) Artificial Neural Network (ANN)
Soma Node
Dendrites Input
Synapse Weights or Interconnections
Axon Output

SIMPLE MODEL OF AN ARTIFICIAL NEURON
A neural net consists of a large number of simple
processing elements called neurons, units, cells or nodes.
Each neuron is connected to other neurons by means of
directed communication links, each with associated weight.
The weight represent information being used by the net to
solve a problem.
Each neuron has an internal state, called its activation or
activity level, which is a function of the inputs it has
received. Typically, a neuron sends its activation as a signal
to several other neurons.
It is important to note that a neuron can send only one
signal at a time, although that signal is broadcast to several
other neurons.

SIMPLE MODEL OF AN ARTIFICIAL
NEURON
The total input I received by soma of artificial neuron
is
I = w1*x1 + w2*x2 + ….+wn*xn
=∑ wi*xi where i=1 to n
To generate the final output Y ,the sum is passed to
filter Φ called activation function or transfer function
or squash function which releases the output
Y=Φ(I) OR Y=F(X)

ARTIFICIAL NEURON MODEL
Neuroni
ai
Output

x0= +1
x1
xm
Input Synaptic
Weights
x2
x3
wi1
wim
Activation
function
f
bi :Bias

ARTIFICIAL NEURON MODEL
n
ai = f (ni) = f (wijxj + bi)
j = 1
An artificial neuron:
- computes the weighted sum of its input (called its net input)
- adds its bias
- passes this value through an activation function
We say that the neuron “fires” (i.e. becomes active) if its output is
above zero.

BIAS
Bias can be incorporated as another weight clamped to a fixed
input of +1.0
This extra free variable (bias) makes the neuron more powerful.
n
ai = f (ni) = f (wijxj) = f(wi.xj)
j = 0

ACTIVATION FUNCTION
Activation functions are an extremely important feature of the
artificial neural networks. They basically decide whether a
neuron should be activated or not. Whether the information
that the neuron is receiving is relevant for the given
information or should it be ignored.

TYPES OF ACTIVATION FUNCTIONS
Identity functions
This function is denoted by f(x) = x for all x. The output
here remains the same as input.
Binary step function
This function makes use of a threshold. A binary step
function with a threshold T is given by
f(x) = 1 if x >= T
f(x) = 0 if x < T

 Bipolar step function
This function makes use of a threshold. A bipolar step
function with a threshold T is given by
f(x) = 1 if x >= T
f(x) = -1 if x < T

Sigmoid functions
Sometimes S shaped functions called sigmoid functions are
used as activation functions which are found useful.
Binary sigmoid
The logistic function, which is a sigmoid function between 0
and 1 are used in neural network as activation function
where the output values are either binary or varies from 0 to
1. It is also called as binary sigmoid or logistic sigmoid.
It is defined as f(x)=1/1+e-x

Bipolar Sigmoid
A logistic sigmoid function can be scaled to have any range
of values which may be appropriate for a problem.The most
common range is from -1 to 1.
It is defined as 2/1+e-x -1
Ramp function
It is defined as
f(x) = 1 if x > 1
f(x) = x if 0<= x <=1
f(x) = 0 if x < 0

PROPERTIES OF ANNS
Learning from examples
– labeled or unlabeled
Adaptivity
– changing the connection strengths to learn things
Non-linearity
– the non-linear activation functions are essential
Fault tolerance
– if one of the neurons or connections is damaged, the whole network
still works quite well
Thus, they might be better alternatives than classical solutions for problems
characterised by:
– high dimensionality, noisy, imprecise or imperfect data; and
– a lack of a clearly stated mathematical solution or algorithm

Comparison between ANN and BNN
Comparison between ANN and BNN
Criteria BNN ANN
Processing Massively parallel, slow but
superior than ANN
Massively parallel, fast but
inferior than BNN
Size 10
11
neurons and
10
15
interconnections
10
2
to 10
4
nodes (mainly
depends on the type of
application and network
designer)
Learning They can tolerate ambiguity Very precise, structured and
formatted data is required to
tolerate ambiguity
Fault tolerance Performance degrades with
even partial damage
It is capable of robust
performance, hence has the
potential to be fault tolerant
Storage capacity Stores the information in the
synapse
Stores the information in
continuous memory
locations

TYPES OF LEARNING
1. SUPERVISED LEARNING
2. UNSUPERVISED LEARNING
3. REINFORCEMENT LEARNING

TYPES OF LEARNING
Supervised Learning---The learning algorithm would fall
under this category if the desired output for the network is
also provided with the input while training the network. By
providing the neural network with both an input and output
pair it is possible to calculate an error based on it's target
output and actual output. It can then use that error to make
corrections to the network by updating it's weights.

TYPES OF LEARNING
Unsupervised Learning---In this paradigm the neural
network is only given a set of inputs and it's the neural
network's responsibility to find some kind of pattern within
the inputs provided without any external aid. This type of
learning paradigm is often used in data mining and is also
used by many recommendation algorithms due to their
ability to predict a user's preferences based on the
preferences of other similar users it has grouped together.

Reinforcement Learning---Reinforcement learning is
similar to supervised learning in that some feedback is
given, however instead of providing a target output a
reward is given based on how well the system performed.
The aim of reinforcement learning is to maximize the
reward the system receives through trial-and-error. This
paradigm relates strongly with how learning works in
nature, for example an animal might remember the actions
it's previously taken which helped it to find food (the
reward).
TYPES OF LEARNING

NEURAL NETWORK ARCHITECTURE
Single-layer feed forward network-Neural network in
which the input layer of source nodes projects into an
output layer of neurons but not vice-versa is known as
single feed-forward or acyclic network. In single layer
network, ‘single layer’ refers to the output layer of
computation nodes

Multilayer feed forward network-This type of network
consists of one or more hidden layers, whose computation
nodes are called hidden neurons or hidden units. The
function of hidden neurons is to interact between the external
input and network output in some useful manner and to
extract higher order statistics. The source nodes in input
layer of network supply the input signal to neurons in the
second layer (1st hidden layer). The output signals of 2nd
layer are used as inputs to the third layer and so on.

Single node with its own feedback-When outputs can be
directed back as inputs to the same layer or preceding layer
nodes, then it results in feedback networks. Recurrent
networks are feedback networks with closed loop. Figure
shows a single recurrent network having single neuron with
feedback to itself.

Single-layer recurrent network-feed forward neural
network having one or more hidden layers with at
least one feedback loop is known as recurrent
network .Below network is single layer network with
feedback connection in which processing element’s
output can be directed back to itself or to other
processing element or both.

Multilayer recurrent network-In this type of network,
processing element output can be directed to the
processing element in the same layer and in the preceding
layer forming a multilayer recurrent network. They
perform the same task for every element of a sequence,
with the output being depended on the previous
computations. Inputs are not needed at each time step.

UNIT- 1
Concept of Computing Systems, Introduction to Soft
Computing, Soft Computing vs. Hard Computing,
Components of Soft Computing, Neural Networks:
Structure and function of Biological Neuron and Artificial
Neuron, Definition and characteristics of ANN, Training
techniques in different ANNs, Activation functions,
Different ANNs architectures, Introduction to basic ANN
architectures: McCulloch & Pitts model, Perceptron
Model, Linear separability, ADALINE and MADALINE.

The McCulloch-Pitts/MP Model of Neuron
The early model of an artificial neuron is introduced by
Warren McCulloch and Walter Pitts in 1943. The
McCulloch-Pitts model was an extremely simple
artificial neuron.
1. It allows binary 0/1 states, bcz it is binary
activated.
2. The neurons are connected by direct weight
graph.
3. The connection path can be excitatory/inhibitory.

The "neurons" operated under the following
assumptions:-
 They are binary devices (Vi = [0,1])
 Each neuron has a fixed threshold, theta values.
 The neuron receives inputs from excitatory synapses,
all having identical weights.
 Inhibitory inputs have an absolute veto power over any
excitatory inputs.
 At each time step the neurons are simultaneously
(synchronously) updated by summing the weighted
excitatory inputs and setting the output (Vi) to 1 if the
sum is greater than or equal to the threshold and if the
neuron receives no inhibitory input.
The McCulloch-Pitts Model of Neuron

Architecture of McCulloch-Pitts Model
From the above fig, the connected path are of two types:
excitatory or inhibitory. Excitatory have positive weight and
which denoted by “w” and inhibitory have negative weight
and which is denoted by “p”. The neuron fires if the net input
to the neuron is greater than threshold. The threshold is set
so that the inhibition is absolute, because, nonzero inhibitory
input will prevent the neuron from firing.

Architecture of McCulloch-Pitts Model
The McCulloch Pitts neuron Y has the activation function:
Y =F (yin) = 1 if y-in ≥ Ѳ
0 if y-in < Ѳ
Where, Ѳ=threshold
Y=net output
By using MCCULLOCH Pitts model we are going to solve
the following logic gates. i. OR Gate ii. NOT Gate iii. AND
Gate iv. NAND Gate v. XOR Gate vi. NOR Gate

Learning: Rules
McCulloch-Pitts Neurons: Obtain the weights by performing
analysis of the problem

The OR gate is a digital logic gate that implements logical
disjunction-it behaves according to the truth table. A high
output i.e. 1 results if one or both the OR GATE inputs to the
gate are high (1).If both inputs are low the result is low (0)[1].
A plus (+) is used to show the or operation. [2] Its block
diagram and truth table is shown by:
Realization of Logic Gates
OR GATE

OR GATE
Net Input = X1*W1+X2*W2
Equation-I
X1*W1+X2*W2< θ
0 < θ
Equation-II
X1*W1+X2*W2>= θ
W2 >= θ
Equation-III
X1*W1+X2*W2>= θ
W1 >= θ
Equation-IV
X1*W1+X2*W2>= θ
W1+W2 >= θ

OR
GATE
Net input yin = x1w1+x2w2
yin = 0*2+0*2
yin = 0+0
0
1. F(yin)< theta and 2. F(yin)>= theta
0<2 output is 0

OR
GATE
yin = 0*2+1*2
yin = 0+2
2
2=2 output is 1

OR
GATE
yin = 1*2+0*2
yin = 2+0
2
1. F(yin)<theta and 2. F(yin)>= theta
2=2 output is 1

OR
GATE
yin = 1*2+1*2
yin = 2+2
4
4>2 output is 1

It is a logic gate that implements conjunction. Whenever both
the inputs are high then only output will be high (1) otherwise
low (0).
Realization of Logic Gates
AND GATE

AND GATE
Net Input = X1*W1+X2*W2
Equation-I
X1*W1+X2*W2< θ
0 < θ
Equation-II
X1*W1+X2*W2>= θ
W2 < θ
Equation-III
X1*W1+X2*W2>= θ
W1 < θ
Equation-IV
X1*W1+X2*W2>= θ
W1+W2 >= θ

AND Gate
yin = 0*1+0*1
yin = 0+0
0
0<2 output is 0

AND Gate
yin = 0*1+1*1
yin = 0+1
1
1<2 output is 0

AND Gate
yin = 1*1+0*1
yin = 1+0
1
1<2 output is 0

AND Gate
yin = 1*1+1*1
yin = 1+1
2
2=2 output is 1

IMPORTANT TERMINOLOGIES
Weight
 The weight contain information about the input signal.
 It is used by the net to solve the problem.
 It is represented in terms of matrix & called as
connection matrix.

Bias
 Bias has an impact in calculating net input.
 Bias is included by adding x0 to the input vector x.
The bias is of two types
Positive bias: Increase the net input
Negative bias: Decrease the net input

Threshold
 It is a set value based upon which the final output is
calculated.
 Calculated net input and threshold is compared to get
the network output.
 The activation function of threshold is defined as
where θ is the fixed threshold value

Learning rate
 Denoted by α.
 Control the amount of weight adjustment at each step
of training. The learning rate range from 0 to 1.
 Determine the rate of learning at each step
Momentum Factor
 Convergence is made faster if a momentum factor is
added to the weight updating process.
 Done in back propagation network.

HEBB LEARNING RULE
 Donald Hebb stated in 1949 that “ In brain, the learning
is performed by the change in the synaptic gap”.
 It is one of the first and also easiest learning rules in the
neural network. It is used for pattern classification.
 It is a single layer neural network, i.e. it has one input
layer and one output layer. The input layer can have
many units, say n. The output layer only has one unit.
Hebbian rule works by updating the weights between
neurons in the neural network for each training sample.

HEBB LEARNING RULE
 Donald Hebb stated in 1949 that “ In brain, the learning
is performed by the change in the synaptic gap”.
 When an axon of cell A is near enough to excite cell B,
and repeatedly or permanently takes place in firing it,
some growth process or metabolic change takes place
in one or both the cells such than A’s efficiency, as one
of the cells firing B, is increased.
 According to Hebb rule, the weight vector is found to
increase proportionately to the product of the input and
the learning signal.

 In Hebb learning, two interconnected neurons are ‘on’
simultaneously. The weight update in Hebb rule is
given by
 Wi(new) = wi (old)+ xi y.
 Bi(new)=bi(old) +y
 It is suited more for bipolar data.
 If binary data is used, the weight updating formula
cannot distinguish two conditions namely
 A training pair in which an input unit is “on” and the
target value is “off” A training pair in which both the
input unit and the target value is “off”.
HEBB LEARNING RULE

FOR II INPUT X1= 1, X2=-1, B=1, Y= -1
W1(NEW) =W1(OLD)+X1Y
=1+1*(-1)
= 1-1
=0
= 1+(-1*-1)
=1+1
=== =2
B(NEW) = B(OLD)+Y
=1+(-1)
=1-1
= 0
New weights and bias are w1=0, w2=2 and b=0

WEIGHT CHANGE
 Del w1= x1y
 =1*(-1)
 -1
 Del w2 = x2y
 = -1*-1
 1
 Del b = y
 =-1

FOR III INPUT X1= -1, X2=1, B=1, Y= -1
WEIGHTS AND BIAS ARE W1=0, W2=2 AND B=0
=0+(-1*(-1))
= 0+1
=1
= 2+(1*-1)
=2-1
=== =1
B(NEW) = B(OLD)+Y
=0+(-1)
=0-1
= -1
New weights and bias are w1=1, w2=1 and b=-1

WEIGHT CHANGE X1= -1, X2=1, B=1, Y= -1
 Del w1= x1y
 =-1*(-1)
 = 1
 Del w2 = x2y
 = 1*-1
 -1
 Del b = y
 =-1

PERCEPTRON MODEL
The perceptron was first introduced by American
psychologist, Frank Rosenblatt in 1957 at Cornell
Aeronautical Laboratory. Rosenblatt was heavily
inspired by the biological neuron and its ability to
learn.

PERCEPTRON MODEL
 Assume we have a single neuron and three
inputs x1, x2, x3 multiplied by the weights w1, w2,
w3 respectively as shown below,

PERCEPTRON MODEL
A perceptron consists of four parts:
1. Input values
2. Weights and a bias,
3. A weighted sum,
4. Activation function.

ROSENBLATT’S PERCEPTRON
The perceptron is the simplest form of a neural network
used for the classification of patterns. The perceptron is
a computational model of the retina of the eye and
hence, is named Perceptron. Basically, it consists of a
single neuron with adjustable synaptic weights and bias.
The perceptron network comprises three units
1) Sensory Unit S,
2) Association Unit A,
3) Response Unit R

PERCEPTRON
The Sensory Unit(S) Comprising 400 photodetectors
receives input of images. and they provides a 0/1 electric
signal as an output. If the input signals exceed a threshold,
then the photodetectors outputs 1 else 0.The photodetectors
are randomly connected to the Association unit (A).
The Association unit Comprises feature demons or
predicates. The predicates examine the output of the
Sensory unit(S) for the specific features of the image. The
third unit.
Response unit(R) Comprises pattern recognizers or
perceptron, which receives the results of the predicates, also
in binary form

TYPES OF PERCEPTRON MODEL
 There are 2 types of perceptron models-
 Single Layer Perceptron- The Single Layer perceptron
is defined by its ability to linearly classify inputs. This
means that this kind of model only utilizes a single
hyperplane line and classifies the inputs as per the
learned weights beforehand.

 Multi-Layer Perceptron- The Multi-Layer Perceptron is
defined by its ability to use layers while classifying
inputs. This type is a high processing algorithm that
allows machines to classify inputs using various more
than one layer at the same time.

SINGLE LAYER PERCEPTRON NETWORK

1. Initialize weights, bias and learning rate

WHY ARE PERCEPTRON'S USED?
 It is typically used for supervised learning of binary
classifiers. This is best explained through an
example. Let’s take a simple perceptron. In this
perceptron we have an input x and y, which is
multiplied with the weights wx and wy respectively,
it also contains a bias.


 Let’s also create a graph with two different
categories of data represented with red and blue
dots.

 the x-axis is labeled after the input x and the y-axis
is labeled after the input y.

 A perceptron can create a decision boundary for a
binary classification, where a decision boundary is
regions of space on a graph that separates different
data points.
 Let’s play with the function to better understand this.
We can say,
 wx = -0.5, wy = 0.5 and b = 0
 Then the function for the perceptron will look like,
 0.5x + 0.5y = 0

LIMITATIONS OF PERCEPTRONS
Perceptrons could not model the exclusive-or function, because its outputs are not linearly separable. Two classes of outputs are
linearly separable if and only if you can draw a straight line in two dimensions that separates one classification from another.

ADALINE NETWORK
 ADALINE (Adaptive Linear Neuron or Adaptive Linear
Element) is a single layer neural network.
 It was developed by Professor Bernard Widrow and his
graduate student Ted Hoff at Stanford University in 1960.
 The difference between Adaline and the standard
(McCulloch-Pitts) perceptron is that in the learning phase
the weights are adjusted according to the weighted sum of
the inputs (the net).
 In the standard perceptron, the net is passed to the
activation (transfer) function and the function's output is
used for adjusting the weights.
 There also exists an extension known as Madaline.

ADALINE NETWORK
 The activation function is the identity function, as opposed to
a threshold function (like the perceptron)
 Adaline learning is based upon gradient descent methods,
that is, the gradient is employed to minimize the least
squared error. This learning method has several names:
LMS (least mean squared) and Widrow-Hoff.
 Adaline learning can easily be turned into discrete
classification learning (just like a perceptron). First, train the
net like any Adaline net, then define a threshold function that
outputs a 1 if the sign of the activation is >=0, and -1
otherwise.

ADALINE NETWORK
 Selection of the learning rate (a) is much more important
than it is for perceptron's. If a is too large, the minimal
surface may be missed, if it is too small then learning can
take a long time. The following has been suggested: if
N=number of test vectors, then the following should be
satisfied: 0,1<=aN,+1,0 . My own experience disagrees
with this estimate; I prefer values of a much smaller.
 Adaline learning **will** converge for datasets that are not
linearly separable.

DELTA LEARNING RULE(WIDROW-HOFF RULE/ LEAST
MEAN SQUARE)

INTRODUCTION TO MADALINE
 Madaline (Multiple Adaline) is using a set of ADALINEs in
parallel as its input layers and a single PE (processing
element) in its output layer. The network of ADALINES
can span many layers.
 For problems with multiple input variables and one
output, each input is applied to one Adaline.
 For similar problems with multiple outputs, Madaline of
parallel process can be used.
 The Madaline network is useful for problems which
involve prediction based on multiple inputs, such as
weather forecasting (Input variables: barometric pressure,
difference in pressure. Output variables: rain, cloudy,
sunny).

ARCHITECTURE OF MADALINE
• A Madaline is composed of several Adalines
• Each ADALINE unit has a bias. There are two
hidden ADALINEs, z1 and z2. There is a single
output ADALINE Y.

SOLVING THE XOR PROBLEM USING MADALINE

Solving the XOR problem using MADALIN

SoftComputingUNIT-1_Neural_Network_Architectures.pptx

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