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But now the most exciting part is coming

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because we're going to be visualizing
the training set results.

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And actually, right now

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we don't have to change anything
except maybe the title here classifier.

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And then here you need to specify kernel

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SVM, kernel SVM
as well as here in the test set.

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So here kernel SVM as well.

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All right.

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Now we can get some coffee and just
execute this and watch the results.

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So we're going to do this.

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We're going to first look at the results

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here and press Command and control.

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Press enter to execute.

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And wow these are the beautiful results
of kernel SVM.

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We can see how it's making this curve here
to classify.

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Well most of the users
in the social network here are since

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we have a two dimensional space
here for the data set,

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that means that the data set was mapped
to a three dimensional space,

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and then on this dimensional space,

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it managed to make the data
linearly separable,

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so that it can find a linear hyperplane
that separates in a much better way.

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The two classes.

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And then it projected back to this
two dimensional space

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to finally obtain this curve here
that separates in a much better way

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the two classes than the linear classifier
you would do with a straight line here,

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as we saw for logistic regression
or SVM, SVM with the linear kernel.

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So that's what happened.

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That's what happened behind the scenes.

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The kernel SVM did an amazing job.

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So we can say congrats.

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Okay, so for those of you
who are seeing this for the first time,

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I'll just quickly remind what it is.

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The points here are the true
observations, the true results.

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So the red points are the users
who didn't buy the SUV in reality,

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and the green points are
the users who bought the SUV.

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And then the regions that we see
here are the prediction regions.

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So the red region is the region
where our model predicts

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that the user doesn't buy the SUV
and the green region is the one

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where our model predicts
that the user buys the SUV.

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So for example, that means
that for this particular user red points,

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which is in the green region,
that makes an incorrect prediction

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because the truth is,
the user didn't buy the SUV.

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But since this user
is in the green region, that means

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that the model predicted
that this user bought the SUV,

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even if that's not
what happened in real life.

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So that's where the graph is about.

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And here is the nonlinear separator
of the kernel SVM algorithm.

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And thanks to this nonlinear separator
our kernel SVM could classify correctly

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those users here,
which wasn't the case for the linear

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separators
because since we had the straight lines,

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it couldn't
catch these users in the right category.

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That is the green category,
because those users

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actually bought the SUV in real life.

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So they should be in the green region.

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And this wasn't the case
for the linear separator.

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And now it's the case

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for the kernel SVM separator
because it's a nonlinear classifier.

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Perfect.

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Now let's have a look at the test results
to see how our model behaves

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on new observations,
to see if it can still classify

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and predict
the results of new observations.

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So we're going to do this. We only have to

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select this.

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Press command and control.

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Press enter to execute.

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And here are the test set results okay.

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So that looks great as well.

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First an important thing to understand
is that the regions that we see

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here are the same regions
as we saw in the data set.

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If you go back to the training set
and then go back to the test set,

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you can see that the regions here
don't change, only the observation

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points change because of course
these are new observation points.

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And so here we can see that

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the kernel SVM did an amazing job
at classifying new observations

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because all these test set observations
here are the users who didn't buy the SUV,

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because the points are red
and they are in the red region.

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That is the region where our classifier
predicts that the users don't buy the SUV.

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So that's correct. Predictions.

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Same for these guys here.

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All the green points
that fall in the green region.

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And of course we have
those incorrect predictions

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which are for example,
this green user here

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who is in the red region
as well as those two green here.

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So that's three.

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Then we have the red users. This one,
this one.

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So 456789 and actually ten.

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We can see that there is a little green
point here hiding behind the red points

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okay. Yeah.

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So that's definitely a very good job.

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You will see how the next classifiers

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will make a different style
of classification of separation.

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You will see that it won't be a curve.

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It will be something else.

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And I will let you find out
about the surprise.

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But definitely
the kernel SVM is a great classifier

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when your data is not linearly separable.

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And we can see how it definitely improved
the results of the linear classifiers

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that we saw
with logistic regression and SVM.

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All right.

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So thank you for watching this tutorial
about kernel SVM.

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I hope you enjoyed it.

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There will be a few more surprises
with the next classifiers, as I told you.

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Until then, enjoy machine learning.