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Hello my friends, and welcome to this new.

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Practical activity of part.

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Nine dimensionality reduction.

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So in the previous. Section
we experimented.

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With PCA.

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Principal component analysis.

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And we indeed.

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Got great results with our.

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One data.

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Set, which will be.

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The same. Data set for this new section.

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Because, you know, we want to compare.

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Several.
Dimensionality. Reduction techniques.

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So there. We go. We're going to see
if we can even.

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Beat PCA, which only had.

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One incorrect. Prediction.

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So we're going to work
with the same data set.

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And therefore
the implementation will be. Exactly.

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The same except one cell.

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Which will be the cell of course where we.

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Implement LDA instead of. PCA. All right.

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Are you ready?

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Let's do this.

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Before we get.

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Into this for the part nine, let's make
sure everyone here is on the same page.

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I gave you the link to this folder
containing all the codes.

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And data sets right before this tutorial.

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So make sure to connect to it.
And now here we go.

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Let's end to part nine
dimensionality reduction.

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And now we're going to go into.

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Section 44.

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Linear Discriminant analysis.

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LDA which will be a new technique.

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Of dimensionality reduction.

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Very powerful as we will see.

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So let's start with.

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Python as.

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Usual. And there.

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We go. This folder just as a.

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Previous one has. Two files.

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This is the implementation.

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And this is the same one data. Set which.

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You know.

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Belongs to one sub business owner
who first.

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Asked you,
you know the most sound to data scientist.

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To do.

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Some cluster to identify
different customer segments.

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For each of.

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You know, the wines of. This data set.

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You know, each row of this data set.

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Corresponds to a certain wine.

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And for each one
we have several wine features.

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Or, you know, characteristics.

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All these up to here.

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And you used.

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All these features to. Identify.

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Those three customer. Segments or,
you know.

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Customer clusters.

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And after which, you know, since.

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This wine shop. Owner was so. Happy and.

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Impressed by your job, well,
then of course the owner asked you to do.

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Another mission, which is the.

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One we're about to do with LDA,
which consists of.

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Building a predictive model, combine
two dimensionality reduction.

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Apply to this data set
so that for each new.

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Wine. That this owner. Has in its wine
shop.

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Well, by.

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Deploying this.

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New predictive model, this owner
will be able to predict which customer.

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Segment this new one belongs to
so that it can recommend this new wine to.

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The right. Customers
and therefore optimize.

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Eventually the sales.

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All right.

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So that's exactly.

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The same data set.
And now let's move on to

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our implementation
linear discriminant analysis.

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Which we. Can either.

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Open with Google Collaboratory as.

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I'm doing it now. Or Jupyter. Notebook.

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And as you notice. I kept this.

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Previous implementation we did on.

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PCA so that. We can, you know, compare.

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The. Results. Indian. Right.

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This is PCA, this is LDA.

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But you know, since this is in read
only mode.

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We're going to. Create now.

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A copy so that we can.

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Re-Implement that.

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Cell that belong to. LDA model.

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So there we go.

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Save a copy in drive.

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This will create a copy. Inside.

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Which will be able to. Re-Implement.

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The LDA model.

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All right.

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And now we can, you know. Close this so.

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That we can have the two implementations
next to each other.

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You know, the two copies.

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And now let's do this.

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Let's quickly.

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Remove, you know, the.

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Cell that. Implements to. LDA. This one.

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And let's.

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Re-Implement this because you know.

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All the rest is the same.

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I will actually.

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Remove. All these outputs here
so that you. Don't.

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See the final. Results.

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And we can keep them as a surprise.

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So let me just remove the outputs too.

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Don't look. Too close.

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And there. We go.

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All right.

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So basically all the cells of.

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This implementation are.

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Exactly the. Same.

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As the previous. One. PCA.

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Except of course this cell.

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That implements. LDA right here.

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So no need to explain all this.

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Plus all these other cells result
from our diverse toolkits.

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So you're. Definitely 100% familiar.

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With them.

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All right.

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So let's do this.

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Let's, you know apply LDA.

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So we're going to create a new code
cell. And there.

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We go.

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Let's implement
linear discriminant analysis.

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So now you have two options. The first.

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And the. Best option is to press.

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Bus on the video
and try to implement this.

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Yourself by of course browsing.

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The. Scikit learn API.

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And find that.

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LDA class that. Can implement that. LDA.

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Dimensionality reduction technique.

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And you will definitely end up. With the.

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Same solution
I will implement in a few seconds.

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And the second option.

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Is of course to, well, not.

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Press pause on the video and implement
with meet the solution in.

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Let's say three seconds, three, two,
one and go, all right, let's do this.

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Let's implement together. LDA.

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So as I've just said.

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We're going to implement LDA.

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Thanks to the secured library.

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Therefore
we're going to start from sklearn

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from which
we're going to get access to this time.

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Not you know.

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The well, let me go to PCA here.

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Not the decomposition module of Cyclegan,
but a new one, which.

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Is very.

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Easy to remember
because. This is actually.

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Discriminant

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underscore analysis.

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Okay. That's another module.

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Of. Scikit-Learn that contains.

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Of course, the class.

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That can implement. LDA and that class.

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Well you know. After this import here
we have to.

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Add the name of this class.

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And the name of.

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This class is capital L.

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And then very simply. Linear.

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Discriminant analysis.

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All right. Very good.
The reason why Google.

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Collab.

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By the way,

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is not helping me with the suggestions
is because the notebook is not running.

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And remember to run the notebook or,
you know, to connect it.

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Well, you need to either. Run any of.

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The first cells or upload the data set.

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So let's do. It right now
so that, you know.

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Google Colab. Can assist me.

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I really love it when it does it.

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So right now
I just clicked on this folder button.

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And then let's click the upload button.

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And we will end up in the
you know. Previous folder.

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For Principal components analysis.

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But let me show you the path again.

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I put my machine learning.

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It is a folder in my desktop.

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So inside we're going to go now
to part nine and then section

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44 Linear Discriminant Analysis and Python
and then one.

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All right.

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So this is exactly
the same dataset as before.

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But I just wanted to. Show you the path.

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All right.
And there we go. We have to one.

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And so now I'm going to show.

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You if I retype this.

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Linear discriminant.

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See now it is helping me.

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So that's maybe better to have, you know.

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This reflex to upload a data
set right at the.

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Beginning. Okay. So linear
discriminant analysis.

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But since.

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This class. Name is actually pretty long
and pretty.

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Not practical, well, let's just,
you know, add a simple shortcut like LDA.

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We can do this. That's fine. And now.

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Let's press.

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Enter to move on to the next step.

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Which is of. Course naturally.

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To create.

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An. Object of this.

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Linear discriminant analysis class.

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All right.

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So of course we're going to call it LDA.

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Right.
And now we're going to call this class.

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And since we gave it the shortcut LDA.

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Well we can simply call.

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LDA this way.

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And now well exactly the same as before.

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This LDA class needs to take.

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As input only one argument,
which is. Exactly.

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The same as before. And also.

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It has the exact. Same name.

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It is n components.

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Which corresponds, of course, to the.

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Final number of. Extracted features.
You want to end up.

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With after applying this.

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Dimensionality reduction technique.

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And of course.

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As I.

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Recommended in the previous section,
we're going to start.

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With two.

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So that we can see if even with only.

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Two extracted features.

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Well, we can get great. Results.

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And if that's the case, we'll not only.

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Will get great results, but also cherry on
the cake will be able to visualize the.

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Results on a nice.

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2D plot.

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Indian. You know.

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Thanks to these two code section.

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All right.

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But right now we need. To finish this.

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So there we go.

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We're going to extract only two features.

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In the end. And to.
Do this we. Need now of.

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Course. To connect our.

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LDA object to our data set.

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But once again separately the training set
and the test set.

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And to connect. It well.

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Of course we need to apply.

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The fit. Transform method.

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To the.

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Training set and then only the transform
method on the test set.

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That's for the exact. Same reason
as. Before.

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It is to.

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Avoid information
leakage from the test set.

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All right. So let's do this.
That's our next step here.

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So we're going to take.

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First X.

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Train right which we're going to. Update.

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To become the new X train.

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After we apply
this LDA feature extraction technique.

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And to do this well we need to take.

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Of course our LDA object from which

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we're going to call the Fit transform.

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Method.

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Which will take as input.

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Well here. Be careful.

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It's not going to be exactly
the same input.

265
00:09:10,600 --> 00:09:12,500
As before. Because you know, with.

266
00:09:12,500 --> 00:09:13,933
PCA the fit.

267
00:09:13,933 --> 00:09:16,800
Transform
method took only Xtrain as input.

268
00:09:16,800 --> 00:09:21,300
Because it only need the features
to apply this PCA.

269
00:09:21,333 --> 00:09:23,200
Dimensionality reduction technique.

270
00:09:23,200 --> 00:09:25,500
But LDA is actually different.

271
00:09:25,500 --> 00:09:28,300
In order to apply the technique,
it needs not.

272
00:09:28,300 --> 00:09:30,300
Only the features but also the.

273
00:09:30,300 --> 00:09:32,000
Dependent variable. Right?

274
00:09:32,000 --> 00:09:33,766
A dependent variable is a required.

275
00:09:33,766 --> 00:09:35,233
Element inside. The.

276
00:09:35,233 --> 00:09:36,633
Equation. Of LDA.

277
00:09:36,633 --> 00:09:38,666
And therefore here in the fit transform.

278
00:09:38,666 --> 00:09:40,466
Method, we need to.

279
00:09:40,466 --> 00:09:44,333
Input not only x train
the old version of xtrain.

280
00:09:44,333 --> 00:09:46,500
Before we apply LDA.

281
00:09:46,500 --> 00:09:48,933
And. Y train.

282
00:09:48,933 --> 00:09:50,933
All right, so be very careful with this.

283
00:09:50,933 --> 00:09:54,033
Whether you choose to apply LDA
or PCA for PCA.

284
00:09:54,033 --> 00:09:56,066
You only have to input X train, and for.

285
00:09:56,066 --> 00:09:58,533
LDA you have to input both the features X.

286
00:09:58,533 --> 00:10:01,033
Train and the dependent variable y train.

287
00:10:01,033 --> 00:10:02,633
All right. Final step.

288
00:10:02,633 --> 00:10:04,633
Well now that we have an.

289
00:10:04,633 --> 00:10:08,100
LDA feature extractor object fitted.

290
00:10:08,133 --> 00:10:12,000
To the training set,
well we can apply. It to the test set.

291
00:10:12,000 --> 00:10:15,200
By only calling the transform
method. Right.

292
00:10:15,200 --> 00:10:16,633
It doesn't make sense to.

293
00:10:16,633 --> 00:10:18,366
Fit it. Again to the. Test set.

294
00:10:18,366 --> 00:10:21,966
Because the test set
is supposed to be new data on which we.

295
00:10:21,966 --> 00:10:24,166
Deploy our model, like in production.

296
00:10:24,166 --> 00:10:27,433
Therefore, we must only apply
the transform method here.

297
00:10:27,666 --> 00:10:29,700
And therefore I'm updating our.

298
00:10:29,700 --> 00:10:31,333
X test variable the.

299
00:10:31,333 --> 00:10:32,166
Following way.

300
00:10:32,166 --> 00:10:34,600
By first calling our LDA object.

301
00:10:34,600 --> 00:10:39,966
From which we're only going
to call the trend form method.

302
00:10:40,400 --> 00:10:42,066
And now, according to you, does.

303
00:10:42,066 --> 00:10:44,033
It need to take only X test.

304
00:10:44,033 --> 00:10:44,700
As input.

305
00:10:44,700 --> 00:10:46,933
Or X test and Y test?

306
00:10:46,933 --> 00:10:48,466
Well, obviously.

307
00:10:48,466 --> 00:10:49,500
It's only need.

308
00:10:49,500 --> 00:10:52,566
To take X test
because we're not supposed to have Y test.

309
00:10:52,566 --> 00:10:54,733
You know X test is like new data.

310
00:10:54,733 --> 00:10:56,766
On which we're going to deploy our model.

311
00:10:56,766 --> 00:10:57,833
Then we'll get. Our.

312
00:10:57,833 --> 00:11:00,633
Predictions and Y original
and we'll compare.

313
00:11:00,633 --> 00:11:02,000
Y prior to white test.

314
00:11:02,000 --> 00:11:05,400
But we're not supposed to have white test
because white is are the real result

315
00:11:05,533 --> 00:11:07,400
that. Contain the hidden truth.

316
00:11:07,400 --> 00:11:08,733
You know, the ground truth.

317
00:11:08,733 --> 00:11:10,033
So of course here.

318
00:11:10,033 --> 00:11:12,400
We only need to. Apply X test.

319
00:11:12,400 --> 00:11:14,566
And the reason why we could enter Y train.

320
00:11:14,566 --> 00:11:18,566
Here is because indeed, we are supposed
to get the ground truth of the.

321
00:11:18,566 --> 00:11:19,366
Training set.

322
00:11:19,366 --> 00:11:20,100
Otherwise we.

323
00:11:20,100 --> 00:11:20,566
Wouldn't be.

324
00:11:20,566 --> 00:11:23,433
Able to. Train our machine learning model.

325
00:11:23,433 --> 00:11:26,066
All right. So X test and there we go.

326
00:11:26,066 --> 00:11:27,500
Not only the implementation.

327
00:11:27,500 --> 00:11:30,166
Of LDA is over, but also the whole.

328
00:11:30,166 --> 00:11:33,000
Implementation. Is over as well.

329
00:11:33,000 --> 00:11:35,166
So now we're going to do this run.

330
00:11:35,166 --> 00:11:36,700
Oh now that we, you know.

331
00:11:36,700 --> 00:11:39,300
Uploaded that. Data set into the notebook.

332
00:11:39,300 --> 00:11:41,000
So we are 100% ready.

333
00:11:41,000 --> 00:11:45,766
And let's just remind what we want
to improve compared to previously.

334
00:11:46,033 --> 00:11:49,666
Well, you know, in the principal component
analysis implementation.

335
00:11:50,000 --> 00:11:50,900
We had.

336
00:11:50,900 --> 00:11:55,200
When obtaining the confusion
matrix, only one incorrect prediction.

337
00:11:55,200 --> 00:11:55,800
Resulting.

338
00:11:55,800 --> 00:11:59,300
In having an accuracy of 97% and in the.

339
00:11:59,666 --> 00:12:01,133
Test set results, which are the.

340
00:12:01,133 --> 00:12:02,633
Most interesting ones.

341
00:12:02,633 --> 00:12:04,866
Well, we had indeed an almost.

342
00:12:04,866 --> 00:12:07,633
Perfect separation. Of the. Three classes.

343
00:12:07,633 --> 00:12:12,733
And now we're going to see. It
with our new feature extracted from LDA.

344
00:12:12,900 --> 00:12:15,933
Well, we can get a perfect separation
of the classes.

345
00:12:15,933 --> 00:12:18,566
And therefore 100%.

346
00:12:18,566 --> 00:12:19,866
Accuracy.

347
00:12:19,866 --> 00:12:20,766
Are you ready?

348
00:12:20,766 --> 00:12:21,933
Let's do this.

349
00:12:21,933 --> 00:12:26,033
3 to 1 go run also.

350
00:12:26,033 --> 00:12:27,800
Now all. The cells. Are running
and there we go.

351
00:12:27,800 --> 00:12:29,300
Oh, there we go.

352
00:12:29,300 --> 00:12:32,800
We just had. A 100%. Accuracy.

353
00:12:32,966 --> 00:12:34,966
So in other. Words logistic.

354
00:12:34,966 --> 00:12:35,933
Regression model was.

355
00:12:35,933 --> 00:12:41,100
Totally able to classify
perfectly our three classes by separating.

356
00:12:41,100 --> 00:12:42,166
Them separately.

357
00:12:42,166 --> 00:12:44,400
And that's exactly
what. We're going to. See.

358
00:12:44,400 --> 00:12:47,300
And you know the. Test set results.

359
00:12:47,300 --> 00:12:48,266
Because indeed.

360
00:12:48,266 --> 00:12:50,600
Well we almost had an incorrect one here.

361
00:12:50,600 --> 00:12:52,800
But as we see the real.

362
00:12:52,800 --> 00:12:53,733
Ones, you know.

363
00:12:53,733 --> 00:12:56,033
Which are all the points here, red.

364
00:12:56,033 --> 00:12:59,133
Green and blue fall into the right.

365
00:12:59,266 --> 00:13:00,366
Prediction regions.

366
00:13:00,366 --> 00:13:02,366
That red prediction region where.

367
00:13:02,366 --> 00:13:05,466
Our model predict that the wine belongs
to customer segment number one.

368
00:13:05,966 --> 00:13:09,600
Then this one where our model predicts
that the wines belong to customer

369
00:13:09,600 --> 00:13:10,800
segment number two.

370
00:13:10,800 --> 00:13:13,600
And finally, this prediction region
where our model.

371
00:13:13,600 --> 00:13:16,266
Predicts
that the. Wines should be recommended to.

372
00:13:16,266 --> 00:13:18,933
Customer. Segment number. Three.

373
00:13:18,933 --> 00:13:20,200
And thanks to these.

374
00:13:20,200 --> 00:13:22,133
New extracted features.

375
00:13:22,133 --> 00:13:23,400
You know, LG one and LG.

376
00:13:23,400 --> 00:13:26,433
Two, well this time
we have a perfect class.

377
00:13:26,433 --> 00:13:27,766
Separator. In other words.

378
00:13:27,766 --> 00:13:30,000
We have a perfect classifier.

379
00:13:30,000 --> 00:13:31,166
And if you're wondering.

380
00:13:31,166 --> 00:13:32,866
How did. LDA managed to.

381
00:13:32,866 --> 00:13:34,533
Separate perfectly the classes?

382
00:13:34,533 --> 00:13:35,666
Whereas, you know, in.

383
00:13:35,666 --> 00:13:38,466
PCA we could see that
it was very difficult to.

384
00:13:38,466 --> 00:13:41,233
Separate.
You know, the wines of the test set.

385
00:13:41,233 --> 00:13:42,566
You know, especially this one.

386
00:13:42,566 --> 00:13:45,533
This one falls in the middle of.
The red. Wines.

387
00:13:45,533 --> 00:13:48,366
Well, that's because the extracted
features are different.

388
00:13:48,366 --> 00:13:51,366
You know,
they're not the same as PC1 and PC2.

389
00:13:51,566 --> 00:13:54,733
They are, you know,
in some other dimensions in which.

390
00:13:54,733 --> 00:13:55,233
Well.

391
00:13:55,233 --> 00:13:56,333
This time it is.

392
00:13:56,333 --> 00:13:59,333
Possible to separate
perfectly the classes.

393
00:13:59,333 --> 00:14:00,900
And that's why this. Time it works.

394
00:14:00,900 --> 00:14:03,900
We are, in other words, in another
dimension.

395
00:14:04,100 --> 00:14:05,100
Okay, so.

396
00:14:05,100 --> 00:14:08,700
I guess now we don't have much
of a challenge because it's impossible.

397
00:14:08,700 --> 00:14:10,666
To beat this. This is just perfect.

398
00:14:10,666 --> 00:14:13,433
I remind that
I did not make this data set.

399
00:14:13,433 --> 00:14:14,266
You know, it's a dataset.

400
00:14:14,266 --> 00:14:15,066
Taken from.

401
00:14:15,066 --> 00:14:17,100
The UCI. ML repository.

402
00:14:17,100 --> 00:14:19,700
So, you know, it's
very close to a real world data set.

403
00:14:19,700 --> 00:14:22,200
But there you go. That shows the power
of this.

404
00:14:22,200 --> 00:14:25,700
Dimensionality reduction technique linear
discriminant analysis.

405
00:14:26,166 --> 00:14:29,400
So now we're going to move on
to the next practical activity.

406
00:14:29,400 --> 00:14:32,800
The next section on this time kernel PCA.

407
00:14:33,033 --> 00:14:33,900
And we can just.

408
00:14:33,900 --> 00:14:37,866
Hope that we'll get, you know,
at least as good results as PCA

409
00:14:37,900 --> 00:14:41,400
or some as good results as LDA. In other.

410
00:14:41,400 --> 00:14:42,966
Words, let's hope that we get.

411
00:14:42,966 --> 00:14:45,966
Maximum one incorrect. Prediction.

412
00:14:46,100 --> 00:14:47,366
So I look forward to seeing you.

413
00:14:47,366 --> 00:14:50,200
In this next section
to implement kernel PCA.

414
00:14:50,200 --> 00:14:52,200
And until then, enjoy machine learning.