Original subtitles

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Hello everyone and welcome to the introduction to support vector machines lecture this lecture will

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discuss the formal definition of support vector machines and then try to get an understanding of the

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intuition behind support vector machines.

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Or as the EMS if you want the mathematics behind this algorithm go ahead and read Chapter 9 of an introduction

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to stickle learning support vector machines or SVM as are also known or supervised learning models of

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associated learning algorithms that analyze data and recognize patterns.

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Their use for classification and regression analysis.

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In this lecture we'll be talking about their use for classification given a set of training examples

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each marked for belonging to one of two categories.

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So binary classification and SBM training algorithm builds a model that assigns new examples.

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Are these test data points into one category or the other.

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Making it a non probabilistic binary linear classifier in SVM model is a representation of the examples

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as points in space maps so that the examples of the separate categories are divided by a clear gap that

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is as wide as possible and that's going to begin to set the intuition for an SVM that we'll see later

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on through some plots and diagrams.

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New examples are then mapped into that same space now predicted to belong to the category based on which

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side of that gap they fall on.

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All right let's go ahead and try to understand the basic intuition through looking at some diagrams

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and some plotted out data.

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Imagine we have the training data below.

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Here we have two classes.

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We have a blue class and a pink class.

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Now what we're going to try to do is a binary classification for new points.

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We want to put a new point on this plot or the horizontal axis is some feature one and the y vertical

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axis is a feature too.

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When we put a new point we wanted the term and does it belong to the blue class or the pink class.

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Intuitively what we could do is draw a separating hyperplane.

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In the case of two that mentions is just a line between the classes.

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However we have lots of options of hyperplane that separate these two classes perfectly.

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Notice that the pink black and green line would all separate the blue and pink training points perfectly

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.

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The question that arises how do we actually choose the line that separates these classes the best.

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What we would like to do is choose a hyperplane that maximizes the margin between the classes.

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So you'll see a diagram.

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Typically it looks like this where you have a separating hyperplane here denoted as the dotted line

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and then a margin that extends out from that hyperplane the vector points at the margin line touch are

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known as support vectors and that's where the name support vector machines come from.

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Here we can see the incircle points that are the support doctors.

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Those are the training points that actually touch those margined lines.

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We can expand this idea to nonlinearly separable data through the use of a kernel trick.

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That means if you take a look at the left hand plot in two dimensions here you may have a X label on

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y label and you'll notice that this data is not linearly separable because it's a loose circle in the

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middle of blue triangles and red outer circle of red circles and there's no way we can draw a straight

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line to separate these classes.

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However through the kernel trick what we do is we end up viewing this in a higher dimension.

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In this case we look at a third Z label over on the right.

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Now it can see that this is separable in the third dimension through another hyperplane.

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You can check out YouTube for a really nice 3D visualization videos explaining this idea and if you

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want the mathematics behind the kernel trick again go ahead and check out Chapter 9 of an introduction

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to school learning.

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Let's go ahead now and jump to our studio and begin to explore an example and then you'll have a project

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to test your understanding of using support vector machines.

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Thanks everyone and I'll see at the next lecture.