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Okay, my friends.

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Are you ready for the final tool
of our data preprocessing toolkit

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feature scaling, which will allow us
to put all our features on the same scale.

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So that's the what?

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And let me quickly remind the why.

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Why do we need to do this?

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Well, that's
because for some of the machinery models,

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that's in order to avoid some features
to be dominated by other features

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in such a way that the dominated features
are not even considered by the machine

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model.

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Now, you also need to be aware
that we will not have to apply feature

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scaling for all the machinery models
just for some of them.

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Therefore, we won't include this
in our data preprocessing template,

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which I will show you by the way,
at the end of this tutorial.

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So we will just add this tool
in the toolkit

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because indeed for a lot of machinery
models, we won't even have to apply

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feature scaling even if we have features
taking very different values.

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For example, if you already know a bit
about the multiple linear

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regression model, you know that
each variable is actually multiplied

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by a coefficient, you know, in the linear
regression equation.

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And so well, you know,

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if you have variables
that take much higher values than others.

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Well, when learning the coefficients,
the coefficients will just compensate

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by taking small values for the variables
that take high values.

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Right.

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We will explain
this more in part to regression.

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But for now, just know that this is a tool
that will be applied

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from time to time for certain machine
learning models, but not all the time.

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As you will see in this course. All right.

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And also in the previous tutorial,
I actually told you that

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I was about to answer
one of the most important questions

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or most frequently asked questions
by the data science community.

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And I will keep, of course, my promise.

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I will answer this when it's time.

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Meaning,
at around the middle of this tutorial.

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But no worries,
all questions about feature scaling

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will be answered
so that you have absolutely no confusion.

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All right,
so we have the what and the why.

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And now let's proceed to the how.

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Meaning
how are we going to apply feature scaling.

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And to answer this question
I'm going to show you the following slides

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which are the main
two feature scaling techniques

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that indeed
put all your features in the same scale.

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And these two techniques are first
standardization,

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which consists
of subtracting each value of your feature

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by the mean of all the values
of the feature, and then dividing

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by the standard deviation,
which is the square root of the variance.

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And this will put all the values
of the feature

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between around minus three
and plus three, right?

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All the different features.

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When you apply this transformation
on all the features of your data set,

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well, all your features will take value
between around minus three and plus three.

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So that's standardization.

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And then you have normalization
which consists of subtracting each value

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of your feature
by the minimum value of the feature,

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and then dividing by the difference
between the maximum value of the feature

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and the minimum value of the feature.

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And so since this is positive,
this is positive.

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And this is always larger than this.

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Well that means that
all the values of your features

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will become between 0 and 1.

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All right.

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So this will result in having

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values of features between minus three
and plus three more or less.

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And this will result in having all the
values of your features between 0 and 1.

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Now the question is also much asked
by the data science community.

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Should we go for standardization
or normalization?

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Well, we're going to be here
very pragmatic.

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Normalization is recommended

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when you have a normal distribution
in most of your features.

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This will be a great feature
scaling technique.

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In that case standardization
actually works well all the time.

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It will do the job all the time.

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Therefore, since this is a technique
that will work all the time,

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and this is a technique that is more
recommended for some specific situations

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where you have most of your features
following a normal distribution.

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Then my ultimate recommendation for sure

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is to go for standardization,
because indeed this will always work.

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You will always do
some relevant feature scaling,

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and this will always
improve the training process.

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So I'm going to teach you this technique.

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I'm going to teach you on how to apply it
on R matrices and features.

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And I'm seeing matrices of features
because now

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we have two matrices of features
which are Xtrain and Exodus.

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And since we understood
in the previous tutorial

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that feature scaling must be applied
after the split, well, you understand

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that we want apply features
getting on the whole matrix of features x,

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but of course
on both x train and X test separately

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and actually
the scaler will be fitted to only X train.

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And then we'll transform X test.

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You know
we'll apply feature scaling on access

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because indeed since X test is something
that's we're not supposed to have

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during the training, but only after like
when going in production.

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Well, we're not allowed to fit our feature
scaling tool on the test set right

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by fitting the feature
scaling to on the test set,

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that means that we're going

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to get the mean of the whole set, and then
the standard deviation in the feature.

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No, we don't have the right to do this
because x

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this is supposed to be something new.

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And therefore we'll
just get the mean of the values in Xtrain

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then get the standard deviation
of the values next train.

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Then apply this formula
to transform all the values in Xtrain

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and then apply that same formula, but
with the same mean and standard deviation

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of the values
in Xtrain to scale the values of x.

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This. It's really,
really important that you understand this.

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And this is once again,
to give some further elements of response

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to that previous question.

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Should we scale before or after the split?

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All right.

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So now that we are all clear on this,
let's proceed to the implementation

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of the how, meaning the implementation
of feature scaling.