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Okay.

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Good. So now we're going to test that out.

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Of course
this whole implementation is over

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because all the rest comes
from our different templates.

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The data preprocessing template,
the data preprocessing toolkit

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and the logistic regression
implementation.

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You know, for the rest.

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So now we can just run the whole code
and see what happens in the end.

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So basically
we are ready to run this code.

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But before let's not forget to upload
the data sets inside this notebook.

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So let's click this button.

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Then please find your machine learning.

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Is that folder on your machine
wherever you downloaded it.

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And then let's go inside.

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Part nine dimensionality reduction.

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Then principal component analysis
then Python.

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And there we go.

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In the Or wine dataset
click open and click okay.

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And now now you're ready to run this

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implementation with simple run all.

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So let's click runtime here.

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And are you ready.

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Let's do this in 321.

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Go. Run all.

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All right.

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Importing the libraries
and importing the data set.

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Or applying the data preprocessing phase.

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Then applying PCA.

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Well it goes way faster than me.

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And what do we end up with?

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Well, we actually end up
with an amazing accuracy of 97%.

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So this business owner,
you know, of this wine shop definitely

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had a great intuition with this idea
of applying dimensionality reduction.

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Because, you know,

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dimensionality reduction doesn't
only consist of reducing the complexity

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of your data set, it can also improve
the final results, you know,

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by combining dimensionality reduction
and your predictive model.

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And here this is exactly what happens.

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We get an amazing accuracy of 97% with
actually only one incorrect prediction.

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Right. And here by the way
this is interesting.

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This is the first time you see a confusion
matrix of three rows and three columns.

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And that of course this time
we have three classes, right.

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We have three customer segments one,
two and three.

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Therefore
we have three classes to predict.

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And so this is the number of correct
predictions of customer segment one.

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This is number of great predictions
of customer segment two

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this is the number of repetitions
of customer segment three.

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And this is the number of incorrect
predictions of customer segment one.

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Right.

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So anyway
only one incorrect prediction in total.

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And that's why
we end up with such a great accuracy.

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And so now we should see
amazing results on the graphs.

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You know, for us
with visualizing the training set results.

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And indeed well, you know,
these are our two principal components

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PC1 on the x axis and PC2 on the y axis.

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And then these are you know,
the different prediction regions.

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This is the prediction region of class
number three where each one of which

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the extracted coordinates of PC1
and PC2 are in this blue

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region will be predicted to belong
to customer segment number three.

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Then this is the prediction
region of customer segment number two,

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where all the wines for which
the PC1 and PC2 extracted features

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that fall in this green region
will be predicted to belong to customer

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segment number two.

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And finally, this prediction region
red corresponds to customer segment number

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one, inside which all the wines of which
the extracted feature is PC1 and PC2

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fall in this region will be predicted
to belong to customer segment number one.

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All right.
And then of course all the dots.

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You know the green dots here,

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the blue dots here and the red dots here
are the real observations.

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You know the real wines
themselves of the training set.

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And so here we can indeed see that we have
a few incorrect predictions.

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But that's only on the training set.

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For example, this is a green wine
meaning a wine that belongs to customer

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segment number two,

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which was predicted by the model to belong
to customer segment number three.

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And these are two other incorrect
predictions of wines

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that belong in reality
to customer segment number two,

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but were predicted by the model
to belong to customer segment number one.

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All right.

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And then another incorrect prediction
here.

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But to look at the incorrect predictions,

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it's more interesting
to check them out on the test set.

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And here is a test set.

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And indeed even on new observations.

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Well our logistic regression
model combined to dimensionality

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reduction was perfectly able to separate
well the three classes.

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And we can see very well that, you know,
incorrect prediction that we saw here

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in the confusion matrix, which is,
you know, right here

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that's the incorrect prediction
and corresponds to a green wine,

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meaning a wine that in reality belongs
to customer segment number two,

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but was predicted by the model
to belong to customer segment number one.

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That's okay.

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You know, any business owner
or data scientist that ends up with such

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result with only one incorrect
prediction can just be super happy.

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But let's see if we can beat that
with our other

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dimensionality reduction techniques
like linear discriminant analysis.

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And you know, to beat that, well,
we'll have to simply get 100% accuracy.

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So we'll see if you know
the linear discriminant,

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which are the extracted features
of the LDA technique, can build, you know,

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a prediction boundary that can separate,
well, all these three classes.

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So this will be quite challenging.

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But this is doable.

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And then we'll check
if we can also do the same with kernel PCA

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which is our final dimensionality
reduction technique.

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All right.

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So as soon as you're ready
for the next technique well I'll be super

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happy to join you in the next practical
activity to implement LDA.

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And until then, enjoy machine learning.