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Hello and welcome to this

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almost final tutorial of the part
one Data Pre-processing.

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I look forward to being well-prepared
with our data to start making our machine

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learning models. It's
going to be very fun.

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We just have to hold on for two more
tutorials and then we're good to go.

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Okay, so today we're going to talk about
feature scaling which is very important

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in machine learning.

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I'm going to explain you why right now.

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So I'm going to go to Google Sheets
to find our data set.

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And here it is.

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Let's explain what is feature scaling
and why we need to do it.

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Okay.

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So as you can see we

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have these two columns age and salary
that contains numerical numbers.

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Let's just focus on the age
and the salary.

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You notice that the variables
are not on the same scale, because the age

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are going from 27 to 50,

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and the salary is going from 40
K to like 90 K.

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So because this age variable and the
salary variable don't have the same scale,

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this will cause some issues
in your machine learning models.

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And why is that.

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It's because you're machine
learning models.

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A lot of machine learning

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models are based on
what is called the Euclidean distance.

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If you remember that back

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from high school, the Euclidean distance
between two data points between two points

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is the square root
of the sum of the squared coordinates.

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Well, actually here it's the same.

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We have two variables age and salary.

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So you can picture age as the x coordinate
and the salary as the y coordinate.

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And in the machine learning models
equations

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sum Euclidean distances
between observation points.

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For example, this one and this one are
computed based on these two coordinates.

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And actually,
since the salary has a much wider range

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of values, it's
because it's going from 0 to 100 k.

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The Euclidean distance
will be dominated by the salary.

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Because, for example,
if we take two observations, for example,

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the this one, the ninth one
and the third one, well the Euclidean

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distance will compute the difference
between this salary and this salary.

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So let's compute it. That's about

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okay.

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So this is

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this one.

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As you can see this is 31,000.

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If you put that in square

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okay.

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Let's see up square that gives this.

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And now let's take
for the same two observations the edges.

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So let's compute equals 48 minus.

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It was this one right 27.

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Okay. That's the difference.

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And now let's take the square equals

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this square 441.

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So you can see very clearly how 
this squared

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difference dominates
this squared difference.

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And that's because these two variables
are not on the same scale.

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So you know in the machine
learning equations it will be like

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this doesn't exist
because it will be dominated by this.

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So that's why we absolutely need
to put the variables on the same scale.

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That is that we are going to transform
these two variables,

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and they're going to have values
in the same range.

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For example they're going to have values
from minus one to plus one here

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and same here minus one to plus one.

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So that we don't get this sort of problem
with a huge number here

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dominating a smaller number here,

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so that eventually
the smaller number doesn't exist.

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There are several ways
of scaling your data.

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A very common one is the standardization,
which means that for each observation

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and each feature, you withdraw
the mean value of all the values

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of the feature, and you divide it
by the standard deviation.

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So that's the first type
of feature scaling.

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And another type is normalization
which means that you subtract

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your observation feature x by the minimum
value of all the feature values.

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And you divide it by the difference
between the maximum of your feature values

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and the minimum of your feature values.

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Don't worry if you're not very comfortable

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with the mathematics here, but
what you need to understand is that we are

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putting all variables
in the same range, in the same scale,

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so that no variable
is dominated by the other.

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Okay, so let's do it right now. Anyway.

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You're going to see how the variables
are going to be transformed.

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You're going to see how they go
from having large

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and very different values
to small and same values.

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So let's move on to our.