00:00So what exactly happens inside this nucleus is when a neuron receives an enough input
00:06signals through dendroids, it is a cell body.
00:10So it is a cell body which is in a biological one we call it as soma.
00:15This is the one which decides whether a total signal is strong enough that you can trigger
00:23a response.
00:23If that combined signal crosses a particular threshold then a neuron fires, so this is
00:30the concept there.
00:31So which means we have seen when you do the summation, when it crosses a certain threshold
00:39how soma the combined effect if it crosses a particular threshold how that neuron fires,
00:46so that part should be mimicked when we build an artificial neuron.
00:51So, that entire is seen inside something called as a node.
00:56So, when we see a node there are two operations that are taking place, the first operation
01:01is summation and the second is how the combined signal if it is greater than a particular threshold
01:09how a neuron fires that concept here is an activation function.
01:13So, here we have a dendroids, dendroids equivalent is an input then we have an cell body, this cell
01:22body we call it as a node which is mainly responsible for performing two operations, one it is used
01:28for an integration it has to take all of the inputs and then we have once when you combine
01:36all of the input when the signal is strong enough then it fires, that concept is mimicked by an activation
01:44function here ok.
01:46And the most important is we have an axon, the terminal connect of this axon we have an
01:53synaptic terminal or synapse.
01:57So, that here axon we call it as an connection and the synapse we call it as an waves.
02:03So, with all of this correlation between biological and then artificial one, now let us look into
02:11what exactly is an ANN that is artificial neural network.
02:15It is an computational model where there we were dealing with the electrochemical signals,
02:21but here it is an artificial one where you will be dealing with the numbers and you will be performing
02:26some you know arithmetic operations.
02:29Therefore, it is an computational model which is basically inspired by this structure of you know
02:37biological neurons only and however, we are seeing the functioning of this biological neuron,
02:42the same thing is been mimicked in an artificial neuron also.
02:46So, how through dendroids the multiple inputs enters through here input enters into the node.
02:54How we have an synapse where you know the strength of the synapse that is the synapse chemical strength
03:03that is equivalent to the weights here, the weights numerical value and then synapse strength
03:11is correlated. So, this summation input is getting multiplied with the weight and you are doing
03:19you will multiply input, multiply them with the corresponding weights and then we will sum them
03:26up and then we will pass it to an activation function. And once you pass it to an activation function,
03:33how biological neuron fires? Similar way here activation function also gives us the
03:40corresponding action. So, this is how the correlation between biological neuron and then the artificial
03:48neuron. So, with this let us get into the most important concept called the mathematical representation
03:56of a neuron. How do we mathematically represent it? So, let us look into, so we have x1, x2, x3,
04:06these are the various inputs that we are taking and each of this is passed to a neuron. So, inside
04:17there
04:17are two mathematical operations that take place, one is the summation part and what exactly you are
04:26what exactly is the summation here? Summation is we are multiplying all of these inputs with its
04:33associated weight. So, we have summation x1, w1, we have x2, w2 and we have x3, w3 if we have
04:43a multiple
04:44and so on up to xn, wn. So, this is what is the first part and we have something called
04:51as bias.
04:52Let us understand this in a while, but let us look into what exactly is this x1, w1, x2, w2.
04:59So,
05:00in short we can write this whole as x into w. Now, suppose here is a small example, suppose if
05:09there
05:09is an requirement where you want to predict if the student, if a student will pass based on 3 input
05:16features. What are the 3 input features? Let us assume we have x1 as number of hours studied, x2 as
05:23attendance percentage and x3 as previous grade. So, for a particular student x1 a number of hours studied
05:31let the value be 8 and attendance percentage is 90 percent and the previous grade the student has
05:38obtained 75 percent. Now, for each of the input, so what is that we have seen? For every of the
05:44input
05:44there is an weight associated with it. So, for hours studied we have 0.4, for the second input we
05:54have the weight 0.3 and for the third input we have the weight 0.2. Now, what is the
06:01mathematical
06:02operation that we are doing? The mathematical operation is x is multiplied with wf. Then if you
06:09look into when we look into this particular, we cannot directly multiply these 2. So, if at all if
06:22you want to perform x into wf, it is not possible. Therefore, what is that we do? We take any
06:28one of
06:29this vector, we are going to take a transpose of it. Either you take x transpose, so that we are
06:36going to
06:36get 8, 90 and 75 and you can multiply it with 0.4, 0.3 and 0.2. We can
06:46do a multiplication or instead of
06:48doing this, we can also do w transpose x. What is the w transpose x? We are taking 0.4,
06:560.3 and 0.2
06:58that is getting multiplied with 0.4.
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