In soft computing, one another important paradigm
of computing is artificial neural network.
So, in this lecture we will introduce the
concept of artificial neural network and it
is uses to solve many problems in different
applications.
So, we know the human is the best creature
in this universe and the main things, that
is intrinsic in the human is basically it
is brain.
Brain is also called central nervous system
due to this very unique characteristics of
the brain, human can do many thing human can
remember, human can reason out, human can
prove theorem, human can solve many problems
human can see the world recognize those things
and many more.
So, behind all these the all performance compared
to the other living things in this world the
human play the brain plays an important role.
Now, as the brain it is also central nervous
system ok; biologically it looks like a gray
matter.
So, that is it why sometimes in medical science
brain is called the gray matters.
Now, in this gray matters there are a lot
of other brain cells are there and any things
from any part of the brain is basically controlled
by this central nervous system.
So, this is this how this brain is also called
the head office of our body.
Now, today we will see exactly how this brain
is composed of and how this brain works and
then how the same thing can be mimicked to
solve our problem in an artificial manner
so, the artificial neural network.
Now, so in the brain in fact, there is a large
collection of brain cells as I told you this
brain cells is, basically the atomic level
the processing units and more precisely this
atomic units is called neuron.
Each neuron is approximately in micron in
length and these are the unique neurons which
basically are the fundamental things of any
what is called a sense processing.
Typically, within a human brain there is around
10 to the power 11 number of neurons.
And these neurons are basically stay there
in a connected manner or you can say in a
network manner and in this network all these
neurons are the units which basically carry
certain pulses.
This pulses basically same as the electrical
pulses.
So, it is also in many ways similar the way
how the current flows from one source to another
destination.
So, these neurons are the cells which basically
propagate the electrical pulses from any part
of our body to the central nervous system
and vice versa.
So, these neurons are the important things
and we will see exactly how a neuron looked
like.
So, in this slides we see one neuron and if
we see these slides then you can understand
it has three different parts.
So, this is the first part, this is the second,
and this is the third part.
Now, this part is called the head of the neuron.
Now so, in this part one is a elongated or
is a soiled portion is called a cell body
of the neuron and it is called the soma and
in the soma there is a core this core is not
exactly the nucleus as it is there in the
body cell.
And, now in the soma there will be hairy like
connection these are called dendrite.
Dendrite is very small thin hair like organs
parts.
And, then the next part it is basically end
or tail of the neuron.
It is called the it is called the synapses.
So, basically the synapses is one part where
it basically meets with other dendrites of
other neuron.
So, it is basically a junction point of meeting
other neuron.
So, other neuron.
So, this is a junction point.
So, there is a synapse is also called junction
point.
Now, between these soma and synapse; there
is a connectivity this connectivity is called
the action.
So, this way the neuron are constructed.
Now, this neuron just like a body cell it
is also a cell.
It is a living cell and the important difference
between the other body cell.
Then this nerve cell is that the other body
cell can go cell division whereas, the neuron
cannot go cell division this means that at
the time of birth a person having number of
neurons can never be increased.
And also if some neurons are damaged or destroyed
it cannot be reproduced unlike the body cell,
if there is a cart or wound it will be healed
and then some new cells will grow to fill
the wound or heal.
So, this is the difference between these cells
and functionally there are many differences
between these neurons and the simple body
cells ok.
So, we will learn about the neuron.
So, neuron is look like this.
And now let us see how this neuron is basically
work there now and this is a very very schematic
of a biological neuron and the different parts
that does know we have discussed about.
So, different part means the dendrite, the
axon, soma, and synapse and here the signal,
signal will flow from dendrite to axon; that
means, from one neuron to the next neuron.
So, this way the signal can propagate it in
a one direction.
So, if; so, there is a basically connection
from every points in our body to the brain
and that is the network is there and for building
such a network the basic unit is basically
this neuron ok.
So, this is the neuron there now here one
question that arises is that; how the signals
flow from one cell to another cell.
Now, in every neuron there is one sort of
fluid is there.
Those fluids are called neurotransmitter.
That means, the body of a neuron is filled
with this liquid it is a neurotransmitter
now a signal whenever it is created this causes
some what is called a different level of concentration.
So, far this liquid neurotransmitter is concerned
for example, if a mosquito bites then the
at the point where the mosquito bites at that
point a signal is created, the signal is basically
is it created means it basically creates a
different level of what is called an neurotransmission
concentration.
Now, this neurotransmitter is basically is
a solution sort of thing we can in a simple
manner we can say is a some concentration
of some cation like any sodium calcium magnesium
all these things are there.
So, these are the basically is ion concentration.
So, whenever a signal or some event occurs
then there is chain in this concentration
level of these ions as a result some voltage
will be developed and due to this voltage
this signal will propagate from one neuron
to next neuron.
So, this is nothing, but an in just like is
an electrical impulse and this electrical
impulse, whenever it is created in a neuron
lasts only for few seconds it is not few seconds
rather it is for a few milliseconds; that
means, whenever that ion concentration difference
occurs it will persist only for a few milliseconds
after that again concentration will be balanced
and there will be no signal or no pulses and
so, so this way the signals are created and
once the signals are created.
Signals will be propagated from one neuron
to another neuron.
Now, in this context one thing we should note
that all signals cannot be propagated from
one neuron to another neuron.
A signals which have certain, what is called
the strength more than a threshold value only
can be transmitted from one neuron to another
neuron.
If the signal strength is less than this threshold
value, the signal will not be transmitted
from one signal to another signal and another
from one neuron to another neuron and another
important thing is that to a neuron the signal
can arrives through the different dendrites
and.
So, many signals whenever coming from the
different neurons to a particular neuron are
summed up summed up at the soma and then summed
up signal is basically propagated via axon
through the synapse to other neuron.
So, these are the things that happens in our
biological neurons.
And this idea is enough to understand how
these things can be considered to solve many
problems.
Now, see these pictures here how the signals
can be.
So, here basically one, here basically some
event occurs.
So, these basically produce some, what is
called electrical pulses will be flow there
come here and then go there this way it will
flow and the signal which is produced here
right.
Because I told you once point here, but in
this point the number of neurons are n fact,
located.
So, so the point where the neurons are located
they will receive this pulse and then pass
through this what is called a neuron and then
summed up here and when this signal strength
is greater than a threshold value will be
passed through these synapse and then from
there it will go to the other neuron.
So, this way the signal propagation takes
place in our neuron.
Now so, this is the idea that is what is called
the biology biological neuron.
In fact, the human brain is basically the
very complex structures and it can be viewed
as a massive, highly interconnected network
of these neurons.
So, gray matter that we just have now learn
about it is basically nothing, but a collection
of neurons, as I told you it is around 10
to the power 11 neurons.
The people who are having more neurons they
have the more processing or computing capabilities
thinking capability they are great scientists
like Albert Einstein.
Now these artificial neural networks is basically
the mimic is a simulation of the biological
neural network which is there and the artificial
neuron is called perceptron.
So, in many book you can see it is call it
is termed as perceptron.
So, neuron or artificial neural.
Network is basically is the basic units which
can solve many problems.
Now, let us see how we can mimic this biological
neuron to our artificial neural neuron or
it is called a perceptron.
Now, here we can see that to this figure can
be considering the two parts: in this first
part we can see it is basically the figure
of a biological neuron and the second part
of this figure is basically.
So, the artificial neuron that is a perceptron
now, here if we can see the input here in
this artificial neural network X 1, X 2 dot
dot X n are the input to the perceptron and
all the input come to this part it is called
the summation unit; it is basically same as
the input from the different part it is coming
like X 1, X 2, X 3 X 4 and coming to this
part and this is the summation unit.
And another important thing that we can note
it here is that.
whenever the signal is coming here it, basically
come with some weight W 1, W 2, W 3, W 4 it
is like this.
So, similarly it is here also the signal that
is coming here with certain weights.
Weights is basically indicates that how the
signal is significant to this neuron?
So, basically all signals those are coming
they are called a weighted signal.
Now, when the weighted signal comes into this
summation unit, basically all the signals
and multiplied by their weights are summed
up here and then total summation of this strength
will be passed through this, this is just
like axon this is just like a axon, and then
come to this point and this point basically;
now the signals which are summed up here comes
to this point is basically same as the synapse
or junction it basically connection to other
neuron.
Now here the signals which are arrived here
right will be check that; whether the signal
strength is greater than the threshold value
or not.
If the signal strength is greater than the
threshold value, that signal will pass to
further, but if it is less than then it will
not pass.
So, so this way we can say this part is same
as this part and this part is same as this
part and this part is this one.
Now, so, this is the biological neuron and
this is artificial neuron and we can see that
how this biological neuron works it can be
considered to work here and basically writing.
So, far the program; that means, computation
is concerned it has to computation.
So, input is there and output is there as
you know in every computation the input and
output is there and this is a system which
basically map given an input to a output and
the mapping.
So, there are two mapping functions or simple
functions are there, one function is basically;
take all these inputs and their weights and
the simple function that it will calculate
is called the sum summation of products of
all weights and their inputs; that means,
X 1 W 1, X 2 W 2, X 3 W 3 and then sum of
all these values.
So, a simple program that can be written which
take input X 1 and W 1, X 2 and W 2 and produce
X 1 W 1 plus X 2 W 2 plus dot dot dot dot
X n W n.
So, this kind of so, this is basically computation
that can take place here in this part a simple
program with a simple loop can be right.
And then here one another program, we can
think about whenever it receive this input;
that means, these are sum of all the inputs
it is there it will check with respect to
some threshold value if the input this sum
is greater than the threshold value then it
will pass.
So, it is basically what if then command is
there a very simple code is there.
So, what I can understand is that the way
this biological neuron works we can write
a simple program to mimic the working of the
biological neuron by means of a perceptron.
So, this is the idea the way the signal is
work.
Now few things are very much pertinent.
So, far this perceptron and our biological
neuron is concerned.
So, as I told you a neuron is a basic unit
and it works as an interconnected form.
So, it is basically network.
So, that is why, It is got a network of neurons
and this network of neurons computes the input
signals, if you pass any signals as an input
to this system.
It will compute the signal and it can has
the characteristic to transport the signals
at a very very high speed and in addition
to this, what is called the working of the
signals few things are very important is that
it can store information it can perceived
and also it can learn automatically.
So, these are the concept that is there, and
we will see how our artificial neural network
the way the biological system works it also
can be implemented and it basically give rise
to the one important theory in the soft competing
artificial neural network.
So, this is the idea about.
So, far the artificial neural network is concerned
and as I told you that this work has certain
computation per thing.
So, input weight are the input and weight
are the input and weight are the input to
the things and this is one module or one function.
Another function is output is there.
So, so this way this neurons neuron system
will work for us and now let us see.
How this neural networks is basically solve
many problems right there.
Now here exactly, again I just want to repeat
the same thing, but in a different way.
So, if this is the input like this is the
input to the system, then reproduces the output
by means of this program.
So, I is that here this I passing there and
here, basically function this function we
called transferring function or transfer function
this function is phi and for this function
I is the input and y is the output.
So, this is the transfer function right.
So, the this I.
So, this function transfer function takes
this I as an input and then produce the output.
Now, again so, this actually we can write
y is a function of I or it is phi of I like.
As you know we have mentioned at the very
beginning of this course any system has the
antecedent and then consequence.
So, it is antecedence and conjugate it basically
maps input to output.
So, mapping so, this way we can understand
that this neuron or is a perceptron rather
how map an input to an output.
Now, again in this processing one important
thing that is there is called the transfer
function.
Now, we have to learn about the transfer functions
and what is the meaning of this?
One here now there are in fact, many many
transfer function known sometimes all these
transfer function is also called thresholding
function.
We usually denote this transfer function as
phi.
Now all these transfer functions is basically
compared the input I with respect to some
threshold value.
We denote this threshold value as theta.
Now the way this transfer function works is
basically is a rule.
That means, if the value of I greater than
theta, then the output is 1, else the output
is 0.
Now, we will learn that the output of a neuron
is either 1 or 0.
It is not necessarily that always 1 or 0.
Sometimes some other value also can be considered
for, but for the sake of simplicity in calculation
usually these two outputs are there.
So, 1 and 0 so; that means, y has the value
either 1 and 0.
So, this phi returns either 1 and 0 and this
is the rule that it follows.
If I greater than theta, then the function
phi I returns 1; if less than or equals to
theta is 0.
So, this is one transfer function that we
have discussed and it follows the rule like
this; and if a transfer function follows this
kind of simple concept, then it is called
a step function.
Also, alternatively this function is called
heavy side function.
Now so, we have learned about the basic or
simple transfer function that is there in
the theory of.
Artificial neural network sometimes this the
step function is also called hard limit transfer
function.
Other than this hard limit transfer function
there is another function also known it is
called the linear transfer function.
Now, here is the picture basically shows how
the hard limit transfer function works and
here is the Signum transfer function or linear
transfer function.
Now, in this case I can see that we see that,
if the input is within this rang, then this
function phi I written 0, and if the input
is beyond this range then output that the
function that returns is 1.
Now, this is the hard limit transfer function.
On the other hand, Signum transfer function.
So, it is basically if the input within these
range it return minus 1 and beyond this range
it will return 1.
So, here in this case the output is minus
1 or plus 1.
So, this is another one so, minus 1 also can
be considered as 0, and this plus 1 also can
be considered one if it is normalized to that
one.
So, anyway so, so Signum transfer function
usually minus 1 and 1 hard limit transfer
function, 1 and 0 although minus 1 to 0 two
levels.
So, two levels can be denoted by 0 and 1 also.
So, these are the two functions are there
in addition to these two transfer function.
There are few more transfer functions are
very important.
These transfer functions are called Sigmoid
transfer function.
The sigmoid transfer function has two versions-
one is called Log-Sigmoid function which basically
takes this form and another is Tan-Sigmoid
function which is basically take this form.
Now, it apparently seems that these two transfer
functions very difficult to compute, but there
is a computation tricks by which all this
calculation can be computed very efficiently,
that we will discuss when we will consider
the application of the neurons to solve problems
anyway.
So, we have learned few transfer functions
which are very popular in the theory of neural
network.
Now, after learning this transfer function.
So, this is a graph actually.
So, this graph basically shows how the transfer
function that we have discussed just now.
Log-Sigmoid and Tan-Sigmoid works is there.
And here the different values alpha can be
decided.
If alpha equals to 0, these basically same
as the sigmoid function that we have discussed.
If alpha value is 1.0 or 10 the sigmoid function
will be like this.
So, for the different value of this one the
sigmoid function will takes place like that.
Now the same thing is applicable to the Tan-Sigmoid
transfer function, here the alpha one important
parameters right which basically decides,
how the transfer functions will behave.
Now so, these are the transfer functions.
Now so, far the ANN is concerned why we should
follow this ANN or the artificial neural network
to solve our problem.
This is because it has very nice mapping capabilities.
That means, any input if it gives to you it
can map to any output and that is with a very
faster rate.
So, that is why any input can be if it is
pattern.
Then it can read result the corresponding
output patterns very effectively.
And another important thing is that; so, far
this neural network is concerned, whatever
the different parameters that we have mentioned
the different parameters means the transfer
function, the different parameter means alpha
in the transfer function or the number of
units or weights in the neuron all these are
the parameters basically which characterized
a behavior of a neuron.
Now, if we can decide the values of this neuron,
then it is enough that the neuron can work
for you.
Now, again this values the all these weights,
transfer function, the threshold values everything
can be learned automatically if you trained
the neuron.
Now, we will discuss about how all these parameters
can be learned automatically.
Now, this is the one capability that the neurons
are having.
That means, automatically it can learn its
value.
And therefore, solve the problem.
So, learning and everything will be discussed
shortly, then we will be able to follow this
concept.
So, this is our advantage and another advantage
is a very much robust, fault tolerance.
Therefore, it can recall full patterns for
incomplete partial or noisy inputs.
ANN can be used to process the information
in parallel at a very high speed and in a
distributed manner.
This is, why this neural systems is effective
for parallel distributed processing and we
can solve any problems which cannot be solved
using the single processing methods.
So, this is the advantage that the neural
artificial neural network is having.
Now so, we have learned about the idea about
the basic units which is there in artificial
neural network.
And in the next lecture, we will learn about
how this neuron can be trained to solve or
learn itself for the different values in it.
Thank you.
