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Hello and welcome
back to the course of Machine Learning.

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Previously we talked about the Support
Vector Machine algorithm.

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And today we're going to talk about the
kernel support Vector machine algorithm.

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And the intuition behind it.

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So as you recall in the support
vector machine situation,

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we had a set of observations, 
which belong to different classes.

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And the point was to find this decision

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boundary between them
so that any future observations

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could be identified
which class they fall into.

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And in this case, we can see that,
there's a decision boundary.

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And the support vector

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machine algorithm tells us
exactly how to find that boundary.

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But what happens
when we cannot find a boundary?

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What happens in a situation
like this, for example.

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What what do we do here?

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We can't just draw a line
through these points, right?

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We can't just separate them
with a straight line.

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We can't separate them
with a horizontal line.

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We can't separate them
with a vertical line.

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Whatever we try to do,
we cannot separate these points

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in the same way that the support vector
machine algorithm, told us to.

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And so what happens in this situation
and why does it happen?

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Well, this happens because in this case,

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the data is not linearly separable.

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So here we've got the two examples
side by side on the left

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the linearly separable data.

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And on the right
the non-linearly separable data.

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And what's the support
vector machine algorithm does is it

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helps us find that decision boundary

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or correctly place that decision boundary.

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But it does have an assumption.

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The assumption is that
the data is linearly separable.

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So basically it's saying that it is
possible to place the decision boundary.

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So support vector machine algorithm
helps us choose the optimal

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decision boundary out of the multiple
decision boundaries that we can draw.

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Whereas in the non linearly separable case
we can't even draw one

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single decision
boundary or linear decision boundary.

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So therefore the support vector machine
algorithm just won't work by definition.

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And so what are we going to do.

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Well this is what this section is about.

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This section is about coming up
with an algorithm that will help us deal

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with situations like that
where we have to extract this class,

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when it is surrounded or,

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in other situations where you can't just
simply just draw a line.

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And the way this section is structured
or the intuition tutorials of this section

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is, first of all, we're
going to explore a method which is called,

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going to a higher dimensional space
where we will learn how we can take,

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this data set and add an extra dimension

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into our, space that we're dealing with

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and make our data, linearly separable.

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So we'll have a look

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at a couple of those examples,
and then we will discuss the kernel trick,

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which allows us to do these things
in a more computationally efficient way

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without having to deal with multiple,
or higher dimensions.

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And finally, we will talk about
the different types of kernels that exist.

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So quite an interesting section
ahead, and I can't wait

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to see you in the next tutorial.
Until then, happy analyzing.