1 00:00:01,320 --> 00:00:08,220 When we start our discussion on maximal marginal classifier, the first thing we need to understand 2 00:00:08,730 --> 00:00:10,770 is the concept of a hybrid plain. 3 00:00:12,730 --> 00:00:19,540 Simply put, a hyper plane is something that divides up be dimensional space in two parts. 4 00:00:21,800 --> 00:00:24,560 Don't be carried away by the word plane in its name. 5 00:00:25,310 --> 00:00:27,680 It is not always a two dimensional plane. 6 00:00:29,330 --> 00:00:31,850 It depends on how many dimensions we are considering. 7 00:00:33,800 --> 00:00:38,210 Let's consider a one dimensional space or it's a one dimensional space. 8 00:00:38,480 --> 00:00:39,040 It's a line. 9 00:00:40,850 --> 00:00:43,730 And how do we separate this line into two parts? 10 00:00:44,600 --> 00:00:45,890 We just need a point. 11 00:00:47,870 --> 00:00:53,320 Now, there's a left part of the line which is left to this point and there is a right part of the line. 12 00:00:54,980 --> 00:00:57,860 This point is a hyperbole for this piece. 13 00:01:00,650 --> 00:01:10,340 If we take a two dimensional space, we can separate it using a line you can see here in this diagram. 14 00:01:11,000 --> 00:01:13,770 We have a two dimensional space, which is a plane. 15 00:01:14,150 --> 00:01:20,900 And we can separated using a lane and there will be a path to the left and a path to the right of this 16 00:01:20,900 --> 00:01:21,260 lane. 17 00:01:22,760 --> 00:01:27,020 So for our two dimensional space, we have a one dimensional separator. 18 00:01:27,470 --> 00:01:28,430 That is a line. 19 00:01:30,170 --> 00:01:35,450 Similarly, if I continue increasing the dimensions of space, let's say a three dimensional space. 20 00:01:36,050 --> 00:01:38,960 It can be separated using our two dimensional plane. 21 00:01:40,340 --> 00:01:44,420 So this concept can be extended to any p dimensional space. 22 00:01:45,020 --> 00:01:52,430 And we will see that there is a hybrid plane of B minus one dimensions, which separates this B dimensional 23 00:01:52,430 --> 00:01:54,170 space into two parts. 24 00:01:56,060 --> 00:02:01,840 But you may be thinking, why are we talking about, B, dimensional spaces and trying to split these 25 00:02:01,840 --> 00:02:02,420 spaces? 26 00:02:03,890 --> 00:02:05,030 Let me explain it to you. 27 00:02:05,270 --> 00:02:10,190 Using an example, suppose I have three variables. 28 00:02:11,060 --> 00:02:17,010 Excellent x2 and the category or the class to which that observation belongs. 29 00:02:19,150 --> 00:02:28,030 These x1, x2 and classes can be anything related to your business, and Edu, x1 and X2 could be height 30 00:02:28,060 --> 00:02:31,600 and weight so students and classes could be weathered. 31 00:02:31,690 --> 00:02:33,610 The student passes or fails. 32 00:02:33,700 --> 00:02:39,760 A sports test X1 and X2 could be the results of two medical tests. 33 00:02:40,480 --> 00:02:46,120 Besides which, we may be trying to classify whether the patient has a heart disease or not. 34 00:02:46,930 --> 00:02:47,800 It could be anything. 35 00:02:48,880 --> 00:02:55,780 Basically we have to predictor variables and one variable is to be predicted, which is also known as 36 00:02:55,780 --> 00:02:57,100 the response variable. 37 00:02:58,030 --> 00:03:04,180 So X1 and X2 are the predictor variables and category is the response variable. 38 00:03:06,370 --> 00:03:13,060 Since we have two predictor variables, we can plot the observations on a two dimensional space such 39 00:03:13,060 --> 00:03:13,630 as this. 40 00:03:15,460 --> 00:03:25,780 We can have X one on the x axis, x2 on the Y axis, and Galut of each point will tell us to which class 41 00:03:25,930 --> 00:03:27,850 that particular point belongs. 42 00:03:29,820 --> 00:03:37,650 So all the blue points belong to one class and all these purple points belong to another class. 43 00:03:39,660 --> 00:03:46,730 I think you can connect the daughter between our hyper plane discussion and this example. 44 00:03:48,240 --> 00:03:56,310 This is basically a p dimensional space here being equal to two, because we have two predictive variables. 45 00:03:56,970 --> 00:03:59,160 And this is a two dimensional space. 46 00:04:01,210 --> 00:04:06,460 We want a hyper plane, which will be a line for this two dimensional space. 47 00:04:07,360 --> 00:04:16,270 So we want such a hyper plane which can divide this space into two parts such that all the blue points 48 00:04:16,420 --> 00:04:20,920 are in one part and all the purple points are in another part. 49 00:04:22,360 --> 00:04:28,570 If I am able to find this iBOT plane, I will have my classified model with me. 50 00:04:30,640 --> 00:04:38,800 Any point which falls on this side of this hyper plane will be classified as blue or class one. 51 00:04:39,520 --> 00:04:48,000 And anything that falls on this side of the hyper plane will be classified as purple or glass to simple, 52 00:04:48,280 --> 00:04:48,590 right? 53 00:04:50,050 --> 00:04:51,030 It is simple to know. 54 00:04:51,760 --> 00:04:53,290 Let's dig deeper in the next. 55 00:04:53,290 --> 00:04:53,710 We do.