1 00:00:01,290 --> 00:00:10,050 ‫Let's start with perceptrons, like in biology, a single cell of our nervous system is called a neuron 2 00:00:11,100 --> 00:00:12,810 ‫in artificial neural networks. 3 00:00:13,500 --> 00:00:17,580 ‫One of the earliest such artificial neuron was a Perceptron. 4 00:00:19,170 --> 00:00:22,020 ‫Perceptron was delivered in 1950s. 5 00:00:23,070 --> 00:00:27,390 ‫Yes, the work on your networks began nearly 70 years ago. 6 00:00:29,240 --> 00:00:35,940 ‫Today, we use other models of artificial neurons, such as sigmoid neurons, to understand sigmoid neurons. 7 00:00:36,210 --> 00:00:37,980 ‫We need to first look at the Perceptron. 8 00:00:40,350 --> 00:00:44,250 ‫Here's a simple pictorial representation of how a Perceptron works. 9 00:00:45,660 --> 00:00:55,620 ‫Perceptron is this circle or a black box, which takes in several binary inputs x1, x2, x3 and so 10 00:00:55,620 --> 00:01:07,140 ‫on till xm and produces a single binary output represented by y, but binary input and binary output. 11 00:01:07,620 --> 00:01:17,280 ‫I mean that these variables can only take two values, for example, zero and one true or false, etc.. 12 00:01:19,170 --> 00:01:27,420 ‫There are several ways in which these x1 x2 x3 can give us the desired output y. 13 00:01:28,710 --> 00:01:29,730 ‫One of these rule is 14 00:01:32,430 --> 00:01:43,470 ‫that we will multiply each of these input values with weights, W1, W2, W3 and then compare. 15 00:01:43,650 --> 00:01:53,040 ‫If the final value of the sum of these products is greater than a threshold value or not, if the 16 00:01:53,040 --> 00:01:58,890 ‫sum value is greater, then the Perceptron gives an output value of one. 17 00:02:00,120 --> 00:02:05,610 ‫And if it is less than threshold, it gives out an output value of zero. 18 00:02:07,690 --> 00:02:10,560 ‫Mathematically, this is how we represent this logic. 19 00:02:11,790 --> 00:02:16,080 ‫This is the submission of weights with feature values. 20 00:02:16,590 --> 00:02:28,700 ‫Basically, this means X1 into W1 plus X2 into W2 plus X3 into W3 and so till Xm into Wm. Basically 21 00:02:30,270 --> 00:02:32,010 ‫The sum of all these product. 22 00:02:32,700 --> 00:02:34,120 ‫Is this left hand term 23 00:02:35,160 --> 00:02:38,130 ‫We compared this sum, with the threshold value. 24 00:02:38,700 --> 00:02:42,600 ‫If this is less than the threshold, we give an output of zero. 25 00:02:43,440 --> 00:02:46,430 ‫If it is more than the threshold, we give output of 1 26 00:02:51,070 --> 00:02:57,010 ‫Let's take a simple example, which may not be very realistic, but you will get the idea of how this 27 00:02:57,010 --> 00:02:58,600 ‫Perceptron functions. 28 00:03:00,940 --> 00:03:05,890 ‫Let's say you want to decide whether you should purchase a particular shirt or not. 29 00:03:08,470 --> 00:03:17,710 ‫You might make your decision by weighing up three factors, whether the shirt is blue or not, whether 30 00:03:17,710 --> 00:03:24,130 ‫the shirt is full sleeve or half sleeve and whether the fabric is cotton or not. 31 00:03:26,530 --> 00:03:30,460 ‫We can represent these three variables using three binary variables. 32 00:03:32,750 --> 00:03:36,440 ‫For instance, X1 is equal to one. 33 00:03:36,680 --> 00:03:43,370 ‫If the shirt is blue and it is zero, if it is not blue, x2 is equal to one. 34 00:03:43,430 --> 00:03:53,330 ‫If it is full sleeved and zero if it is half sleeved and x3 is equal to one for cotton fabric and zero for 35 00:03:53,560 --> 00:03:54,530 ‫non-cotton fabric. 36 00:03:57,170 --> 00:04:04,730 ‫Now, suppose that you absolutely adored Blue-colord shirts and you would prefer full sleeved cotton 37 00:04:04,730 --> 00:04:11,480 ‫fabric shirts but sleeve length and cotton fabric is not as important as the color of the shirt. 38 00:04:13,580 --> 00:04:19,280 ‫So here are sample weights of importance that you assign to these features. 39 00:04:20,900 --> 00:04:24,520 ‫You give weight of seven to the shirt color. 40 00:04:25,820 --> 00:04:29,480 ‫I have replaced the value of W1 with this number seven. 41 00:04:30,920 --> 00:04:36,530 ‫We assign a weight of four to sleeve length and a weight of two to the fabric. 42 00:04:38,120 --> 00:04:45,200 ‫Finally, we also take a threshold value of 8 to decide whether to purchase the shirt or not. 43 00:04:47,120 --> 00:04:53,780 ‫With these choices of weights and threshold, let's see which of these 3 shirts would we buy. 44 00:04:56,330 --> 00:05:03,590 ‫So for this first shirt, we have blue in the first column, which signifies the color of the shirt. 45 00:05:04,100 --> 00:05:04,940 ‫It is half sleeved. 46 00:05:05,240 --> 00:05:06,590 ‫So half in the second column. 47 00:05:07,010 --> 00:05:09,680 ‫It is non cotton, so non cotton in the third column. 48 00:05:09,980 --> 00:05:10,910 ‫which is for fabric. 49 00:05:11,930 --> 00:05:18,260 ‫The fourth column is for calculation of sum, as I told you previously. 50 00:05:18,710 --> 00:05:25,920 ‫We calculate the product of weights with the features, add them together to find the calculated sum 51 00:05:27,860 --> 00:05:28,850 ‫in the Fifth Column. 52 00:05:29,180 --> 00:05:34,790 ‫We have written the threshold value that is predecided. In the sixth column. 53 00:05:35,030 --> 00:05:38,540 ‫We compare this sum value with the threshold value 54 00:05:38,960 --> 00:05:42,110 ‫If the sum is greater than threshold, we will buy the shirt. 55 00:05:42,440 --> 00:05:45,470 ‫If the sum is less than threshold, we will not buy the shirt. 56 00:05:47,120 --> 00:05:49,880 ‫So let's let's see what happens with this first shirt. 57 00:05:50,990 --> 00:05:54,350 ‫The first shirt is blue in color, for blue. 58 00:05:54,740 --> 00:05:57,890 ‫We have x1 value of one for not blue. 59 00:05:57,980 --> 00:05:58,970 ‫It would have been zero. 60 00:05:59,660 --> 00:06:03,350 ‫So x1 is 1. x2. 61 00:06:03,890 --> 00:06:07,100 ‫We just leave is zero because it is half sleeved. 62 00:06:08,510 --> 00:06:11,200 ‫Fabric is non cotton which is again zero. 63 00:06:13,670 --> 00:06:16,060 ‫We find out the sum product seven. 64 00:06:16,480 --> 00:06:25,040 ‫It is weightage for color multiply by the value of X1, which is one plus four. 65 00:06:25,080 --> 00:06:30,630 ‫weightage for sleeves multiplied by the value of X2, which is zero because it is half sleeved. 66 00:06:31,250 --> 00:06:38,330 ‫Plus two, which is weightage for fabric multiplied by the value of fabric, which is zero because 67 00:06:38,330 --> 00:06:39,590 ‫it is not cotton. 68 00:06:41,030 --> 00:06:43,160 ‫The final summary we get is seven. 69 00:06:44,120 --> 00:06:48,100 ‫We compare this sum value with the threshold value, which is eight. 70 00:06:48,970 --> 00:06:50,630 ‫The sum is less than eight. 71 00:06:51,470 --> 00:06:53,900 ‫So we are not going to buy this shirt. 72 00:06:56,360 --> 00:06:58,670 ‫Let's do this activity for the second shirt. 73 00:06:59,090 --> 00:07:03,820 ‫The second shirt is blue colored, full sleeved and non cotton fabric. 74 00:07:05,000 --> 00:07:13,110 ‫If you repeat the calculation, the only difference is going to be the value of X2, for full sleeve 75 00:07:13,140 --> 00:07:14,570 ‫shirt X2 will be one. 76 00:07:14,960 --> 00:07:17,180 ‫So seven plus four is going to come out. 77 00:07:17,180 --> 00:07:17,960 ‫as eleven. 78 00:07:18,770 --> 00:07:19,970 ‫Eleven is more than eight. 79 00:07:20,210 --> 00:07:21,590 ‫So we are going to buy the shirt. 80 00:07:24,140 --> 00:07:30,830 ‫Similarly for the third shirt, which is not blue, full sleeved, cotton shirt, sum comes out to be six, which 81 00:07:30,830 --> 00:07:34,340 ‫is less than eight, which means that we are not going to buy this shirt. 82 00:07:35,840 --> 00:07:42,530 ‫Can, you know, see how Perceptron is deciding the output that whether you will buy a shirt or not? 83 00:07:44,420 --> 00:07:50,370 ‫It is just multiplying the values of the feature with corresponding weight and checking the sum against 84 00:07:50,370 --> 00:07:51,320 ‫the threshold value. 85 00:07:51,950 --> 00:07:56,350 ‫If the sum is larger than the threshold, it gives one output. 86 00:07:56,660 --> 00:07:59,420 ‫If it is smaller, then it gives other output. 87 00:08:00,950 --> 00:08:06,710 ‫This is a very simple example which I have given to make you understand how a Perceptron is working. 88 00:08:07,400 --> 00:08:14,270 ‫In reality, we solve much more complex problems in which we have numerous input variables and many 89 00:08:14,270 --> 00:08:14,990 ‫conditions. 90 00:08:15,500 --> 00:08:18,490 ‫We will get to them in the due course of the lectures. 91 00:08:19,940 --> 00:08:28,010 ‫As you can see, a Perceptron requires these weights and this threshold value to give out an output. 92 00:08:29,540 --> 00:08:32,510 ‫And how will Perceptron get devalues of these parameters? 93 00:08:33,920 --> 00:08:38,420 ‫One way is we give the values, in which case it is not learning. 94 00:08:38,960 --> 00:08:48,230 ‫It is simple programming the other ways learning where we provide de Perceptron with historical data 95 00:08:48,500 --> 00:08:52,460 ‫of which shirts were selected and which shirts were rejected. 96 00:08:53,610 --> 00:08:55,970 ‫And Perceptron decides the weight and 97 00:08:56,090 --> 00:09:04,910 ‫threshold value, according to that previous data, by the way you can get different models, by changing 98 00:09:04,910 --> 00:09:05,510 ‫weights and 99 00:09:05,550 --> 00:09:05,830 ‫threshold 100 00:09:07,600 --> 00:09:17,990 ‫For example, if you want to select a shirt, which is blue full sleeved and cotton only and no other 101 00:09:17,990 --> 00:09:18,650 ‫combination. 102 00:09:19,660 --> 00:09:27,980 ‫this set of weights and threshold ensures that. Try it out you will see only blue cotton full sleeve 103 00:09:28,040 --> 00:09:32,930 ‫shirt will be selected and no other shirt will pass through. 104 00:09:35,750 --> 00:09:37,310 ‫So that's about it. 105 00:09:38,540 --> 00:09:41,600 ‫This is a basic introduction to the Perceptron. 106 00:09:42,080 --> 00:09:45,260 ‫We will extend this idea of Perceptron in the next lecture.