00:00change 0.2. So, now we are updating w1 to 0.3, we have updated w1 to 0.3. So,
00:11similar
00:11way you can check for w2 and you can see how we are going to.
00:18So, this is for one single epoch which I have solved the problem, I will be pausing here
00:25for a few seconds where I want you to complete it for one more iteration, for one more epoch
00:33and then see is there any changes in the weight, how long you will continue to do this, can
00:39you see here in the error everything should be 0. So, here we still have one of the sample
00:45which is still getting misclassified. So, until this column error column turns to be 0, you
00:52will be repeating this process. So, towards the end once you complete the solving the entire
00:57ok, let me go back and then show once you complete the first epoch then the final weights what
01:05we have got is 0.3 and 0.5. So, for the next epoch the weights that we consider our
01:13problem
01:14statement will be something like this, the weight will be 0.3 and 0.5 and then once again
01:20you will pass 00, you will check for 01, we will check for 10 and we will check for 11
01:26and
01:27then we will solve the entire we are going to get this table.
01:30Then we are seeing that still there is some misclassification. So, for the next epoch whatever
01:36is the last updated weight that will be used for the next one. So, for this you will have
01:43the graph something like this, you will have the weights 0.5 and 0.5 and then you check,
01:51you repeat this you will see all the points are correctly classified. Therefore, what we
01:57are understanding by solving this particular problem is initially the weights that we had
02:01considered was 0.1 and 0.3. But after we have solved the entire problem, after we have updated
02:09the weights we have understood that 0.1 and 0.3 are not the correct weights, the correct
02:15weights are 0.5 and 0.5. This is how you will update the weights using a perceptron learning
02:24rule ok. So, with this we have come to the end of a theory part of single layer perceptron
02:32where we will see what are the limitations of single layer perceptron, why we will not
02:38use single layer perceptron more to solve a real world problems. First of all from all
02:43the concepts, all the topics that we have seen what we have understood, single layer perceptron
02:49can only classify the data which is linearly separable one. What is linearly separable data?
02:55where you will have a straight line, you can able to separate 2 classes using a straight
03:02line or a hyperplane. Now, but what if we have a data where you cannot be able to separate them
03:09using an you know straight line, then single layer perceptron cannot be solved which is that one
03:15example when you take an XOR, XOR problem statement you cannot separate them using a straight line.
03:22So, because of this this is the first limitation and what is the second limitation? It is a primarily
03:28designed for a binary classification problem, but what if in a real world what if you have
03:35a multi class classification problem and you know what if you want to solve a regression problem,
03:41then you cannot directly use a single layer perceptron the original model that is being designed as
03:47it is we cannot use, we have we can use by using certain modifications or by doing a certain
03:52extension. So, this is the second limitation of single layer perception and the third and the most
03:59important one is you have seen from both the problems what we have solved using a single layer
04:07perceptron we had assumed the weights. So, what if the initial assumption weights are too large or it is
04:15too small or you have not properly chosen the weights, then you will be keep solving the problem you know
04:23it will take long you know it takes more time to train the model. So, this is the and it
04:31may even get stuck
04:32in a wrong decision boundary. So, it may never reach the correct one. So, it is very very sensitive,
04:38the performance of single layer perceptron is very sensitive to the initial values of its weights.
04:45So, these are certain limitations of single layer perception. So, with this as I told we have come
04:53to an end of a single layer perception. So, before we move into the next topic, let us quickly have
05:00a
05:01summary of the entire what we have learnt. So, this is primarily been inspired from a biological neural
05:08system and where the inputs are entered into an neuron and here the inputs are x1, x2 and so on
05:18up
05:18to xn, these inputs are taken from the data set. With every of the input there will be a weights
05:24that are
05:25associated. So, this is an cell body which we call it as an neuron primarily responsible for performing
05:32two mathematical operations. The first mathematical operation is it performs the summation of input
05:39multiplied with the weight and then we will have an you know x w transpose x and then you will
05:47be adding
05:47it to a bias term and whatever the resultant value that we are getting that resultant is passed to
05:53an activation function. And since it is an single layer perceptron, the activation function that
06:00we will be using here is an step activation function or an threshold activation function.
06:06Now, the output of the neuron, since it is mainly used to solve a binary classification, you will have
06:14a value either 0 or 1. So, once you get the output, the next step we will be calculating the
06:21error.
06:21How is that we calculate the error? The error is given by the formula target minus computed. So,
06:29this is the formula that is used to calculate the error. Now, once the error is calculated,
06:33we will calculate delta w change in the weight. So, how much change you need to do for the weight?
06:40So, delta w is given by the formula learning rate and that is multiplied with the error and that is
06:47multiplied with the associated input x i. Now, this is given to a formula w nu is equal to w
06:56old plus
06:57change in this weight delta w. So, that becomes a new weights for the next input or for the next
07:05epoch.
07:06So, this is what is the total summary of a single layer perceptron. So, with us, we have come to
07:14an
07:14end of an theory session. Now, let us look.
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