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These are the user uploaded subtitles that are being translated: 1 00:00:00,690 --> 00:00:05,750 Hello everyone and welcome to the introduction to support vector machines lecture this lecture will 2 00:00:05,760 --> 00:00:10,140 discuss the formal definition of support vector machines and then try to get an understanding of the 3 00:00:10,140 --> 00:00:12,300 intuition behind support vector machines. 4 00:00:12,330 --> 00:00:19,170 Or as the EMS if you want the mathematics behind this algorithm go ahead and read Chapter 9 of an introduction 5 00:00:19,170 --> 00:00:26,460 to stickle learning support vector machines or SVM as are also known or supervised learning models of 6 00:00:26,460 --> 00:00:30,460 associated learning algorithms that analyze data and recognize patterns. 7 00:00:30,520 --> 00:00:33,380 Their use for classification and regression analysis. 8 00:00:33,600 --> 00:00:40,350 In this lecture we'll be talking about their use for classification given a set of training examples 9 00:00:40,470 --> 00:00:43,370 each marked for belonging to one of two categories. 10 00:00:43,470 --> 00:00:49,340 So binary classification and SBM training algorithm builds a model that assigns new examples. 11 00:00:49,340 --> 00:00:53,010 Are these test data points into one category or the other. 12 00:00:53,010 --> 00:01:00,690 Making it a non probabilistic binary linear classifier in SVM model is a representation of the examples 13 00:01:00,720 --> 00:01:07,020 as points in space maps so that the examples of the separate categories are divided by a clear gap that 14 00:01:07,020 --> 00:01:12,990 is as wide as possible and that's going to begin to set the intuition for an SVM that we'll see later 15 00:01:12,990 --> 00:01:15,390 on through some plots and diagrams. 16 00:01:15,390 --> 00:01:21,180 New examples are then mapped into that same space now predicted to belong to the category based on which 17 00:01:21,180 --> 00:01:24,030 side of that gap they fall on. 18 00:01:24,030 --> 00:01:29,040 All right let's go ahead and try to understand the basic intuition through looking at some diagrams 19 00:01:29,130 --> 00:01:31,160 and some plotted out data. 20 00:01:31,190 --> 00:01:34,400 Imagine we have the training data below. 21 00:01:34,450 --> 00:01:36,480 Here we have two classes. 22 00:01:36,480 --> 00:01:39,160 We have a blue class and a pink class. 23 00:01:39,270 --> 00:01:44,070 Now what we're going to try to do is a binary classification for new points. 24 00:01:44,070 --> 00:01:51,480 We want to put a new point on this plot or the horizontal axis is some feature one and the y vertical 25 00:01:51,480 --> 00:01:53,470 axis is a feature too. 26 00:01:53,820 --> 00:01:59,030 When we put a new point we wanted the term and does it belong to the blue class or the pink class. 27 00:01:59,190 --> 00:02:03,780 Intuitively what we could do is draw a separating hyperplane. 28 00:02:03,810 --> 00:02:08,720 In the case of two that mentions is just a line between the classes. 29 00:02:08,720 --> 00:02:15,390 However we have lots of options of hyperplane that separate these two classes perfectly. 30 00:02:15,390 --> 00:02:22,290 Notice that the pink black and green line would all separate the blue and pink training points perfectly 31 00:02:22,290 --> 00:02:23,430 . 32 00:02:23,430 --> 00:02:29,570 The question that arises how do we actually choose the line that separates these classes the best. 33 00:02:29,910 --> 00:02:35,740 What we would like to do is choose a hyperplane that maximizes the margin between the classes. 34 00:02:36,120 --> 00:02:37,350 So you'll see a diagram. 35 00:02:37,350 --> 00:02:42,840 Typically it looks like this where you have a separating hyperplane here denoted as the dotted line 36 00:02:43,080 --> 00:02:49,830 and then a margin that extends out from that hyperplane the vector points at the margin line touch are 37 00:02:49,830 --> 00:02:55,080 known as support vectors and that's where the name support vector machines come from. 38 00:02:55,080 --> 00:02:59,280 Here we can see the incircle points that are the support doctors. 39 00:02:59,280 --> 00:03:04,470 Those are the training points that actually touch those margined lines. 40 00:03:04,980 --> 00:03:11,310 We can expand this idea to nonlinearly separable data through the use of a kernel trick. 41 00:03:11,310 --> 00:03:18,000 That means if you take a look at the left hand plot in two dimensions here you may have a X label on 42 00:03:18,000 --> 00:03:24,930 y label and you'll notice that this data is not linearly separable because it's a loose circle in the 43 00:03:24,930 --> 00:03:30,930 middle of blue triangles and red outer circle of red circles and there's no way we can draw a straight 44 00:03:30,930 --> 00:03:33,210 line to separate these classes. 45 00:03:33,210 --> 00:03:38,970 However through the kernel trick what we do is we end up viewing this in a higher dimension. 46 00:03:39,000 --> 00:03:43,540 In this case we look at a third Z label over on the right. 47 00:03:43,680 --> 00:03:49,020 Now it can see that this is separable in the third dimension through another hyperplane. 48 00:03:49,020 --> 00:03:54,000 You can check out YouTube for a really nice 3D visualization videos explaining this idea and if you 49 00:03:54,000 --> 00:03:58,890 want the mathematics behind the kernel trick again go ahead and check out Chapter 9 of an introduction 50 00:03:58,980 --> 00:04:01,250 to school learning. 51 00:04:02,490 --> 00:04:07,320 Let's go ahead now and jump to our studio and begin to explore an example and then you'll have a project 52 00:04:07,320 --> 00:04:10,770 to test your understanding of using support vector machines. 53 00:04:10,770 --> 00:04:13,270 Thanks everyone and I'll see at the next lecture. 6200