00:00value, the previous bias value was 0.2 plus the learning rate 0.1 into error is 1. So,
00:08the bias what we are getting is 0.3. With this the new parameters W are 0.1 minus 0
00:17.4
00:19and minus 0.1 and bias is 0.3. Can you see both the values are here? First initial values
00:26what we had considered W1, W2 are 0.2 and minus 0.5 and bias value is 0.1 and
00:35after updating
00:38we have got W value as 0.3 and minus 0.3 and we have updated the bias. With that
00:44we have
00:44seen whether the value what we are getting is right, no we were not getting correct values
00:48till there was an error. Again we went back and then we have updated the weights.
00:55So, let us see by updating the weights now are we getting the correct. So, let us go
01:02back and then calculate. So, what is x1 and x2? The x1 and x2 is 1 and 2. What is
01:11W? The
01:12W value what we have calculated is 0.4 minus 0.1 and what is the bias new bias that
01:18we have
01:19calculated is 0.3. So, with this we are calculating z. How will you calculate z? x1 W1 plus x2
01:27W2
01:28plus bias. What is x1 1? 0.4 plus x2 2 minus 0.1 plus bias 0.3. So, it
01:39is 0.4 this is minus
01:400.2 plus 0.2 plus 0.3. So, z value what we got is 0.5. This is z
01:47value that we have got.
01:48Now, once we get the summation you will be passing it to an activation. What is activation?
01:53So, if the value is go back and then see what is the if the value is less than or
01:58equal to
01:590 it is 0. But our value what we got is greater than. So, therefore, the y hat is 1
02:06the predicted
02:06value is 1. So, now you will calculate the error. What is the error? The error is a target minus
02:13computed. Target value is 1 computed value. So, error value what we got is 0. So, when the
02:19error value is 0 that means now the weights that you have taken are the correct weights. Therefore,
02:28the correct parameters are w the w value is 0.4 and minus 0.1 and the bias value is
02:360.3. Therefore,
02:39now how do the final decision boundary looks like? So, our summation is w transpose x plus b right. So,
02:48this the final decision boundary by end of training what we are going to get is the way it is
02:55x1 w1
02:57plus x2 w2 plus bias right. So, what is our w1? It is 0.4. What is w2? It is
03:14minus 0.1 and what is the bias? 0.3.
03:18So, can we write our equation 0.1 x2 plus 0.3 will be 0. This is the final decision
03:28boundary
03:28that we have got by end of a training. Now, what is the role of this? Why do we require
03:34this?
03:35Now, see once the training is done this is what the model is learning. By end of a training why
03:42you
03:43feel that the training is completed because we have run it run it for certain epochs and then we
03:47are seeing that the error is also 0 now. So, we are stopping the training and this is the decision
03:52boundary that we got. Now, let us assume during the testing phase for our training we had taken
04:01the input 1 and 2 and we were knowing the ground truth is 1. Now, during the testing phase let
04:07us
04:07assume we got input 1 and 2 and we want to know what is the output, we want to know
04:12this. So,
04:13with this what is x1? The new x1 value is 2 and x2 value is 1 and where are these
04:21values coming from?
04:22During the testing the new sample has entered and then we want to see what is the prediction
04:27for this particular input. So, how do the system works? So, during training it has already built the
04:33decision boundary. So, for that you just substitute and then see what is the value that we are going
04:43to get it is. So, here since definitely the z value is 1 correct. So, which is z value is
05:011, 1.0 yeah.
05:03So, now since the value is greater than 0, the y hat value is 1. So, for the new input
05:11what model
05:11is going to predict is 1. So, this is what the model this is how the model is going to
05:17predict.
05:18If you want you can take one more example, let us assume the new example the new sample what we
05:23got
05:23is 0 and 5 substitute values back into this calculate the z 0.4 into 0 minus 0.1 into
05:335 plus 0.3. So,
05:36when we calculate the z value what we are going to get is minus 0.2 which is less than
05:410. So, for this
05:42the predicted value will be 0. Suppose if an input is 0 and 5 the model is going to predict
05:49the output as
05:500. So, with this we have come to an end of session where we have learnt in detail about a
06:00single layer
06:00perceptron and then we have seen we have learnt the algorithm of single layer perceptron. Thus,
06:08we will be stopping the session and in the upcoming session we will be learning the different types
06:16of perceptrons. What are the limitations of this single layer perception and then let us also learn
06:23the single layer perception with one more numerical example that is what you are going to study in the
06:29next session. Thank you.
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