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Hello and welcome back.

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Today we've got an important tutorial.

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We're talking about feature scaling.

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Now before we dive into the technical
aspects of feature scaling,

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I would like to present you with an image
that hopefully will help

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you remember
what feature scaling is applied to.

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Now, even without

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knowing anything about feature scaling,
please remember that features killing

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is always applied to columns, so feature
scaling would be applied to this column.

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To this column. To this column.

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To this column.

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Feature
scaling is never applied across columns,

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so you wouldn't apply feature
scaling to data inside a row.

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Just to remember.

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Feature
scaling is always applied to columns.

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Now with that out of the way,
let's have a look at what feature scaling

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actually is.

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So there are multiple types of feature
scaling multiple techniques.

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We're going to look at the two main ones.

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normalization and standardization.

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Normalization is the process
of taking the minimum inside

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a column, subtracting that minimum from
every single value inside that column,

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and then dividing by

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the difference
between the maximum and the minimum.

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So basically every single value
in a column is adjusted this way.

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And you will end up with a new column
or an adjusted column

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with values which are all between 0 and 1.

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Standardization, on the other hand, is
the process is similar,

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but instead of subtracting the minimum,
we subtract the average

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and we divide by the standard deviation.

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As a result, all of the values,
or almost all of the values inside

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the column will be between -3 and 3.

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if you have some extreme values
or some outliers,

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then they can end up outside
of these minus three and three boundaries.

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So that is normalization standardization.

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In the practical tutorials with understand
you'll be looking at standardization.

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And for simplicity's sake

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in these intuition terms
we'll have a look at normalization.

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So let's imagine we have a data set
where we have two columns,

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annual income of a person and their age.

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Just two simple days
with those two columns.

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And again, for simplicity's
sake, we're only going to have three rows.

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We're going to have a blue person,
a purple person and a red person.

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Now here, is the data.

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We have blue person making $70,000

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a year and their age is 45 years.

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purple person makes $60,000
a year and their age is 44 years,

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and red person makes $52,000 a year,
and their age is 40 years.

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Now, the task at hand
is going to be slightly different

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to the regressions and, classifications
that we've been discussing.

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The task at hand is to,

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see which of the two people

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the purple person is most
similar to, just based on this data.

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Would you say that the purple person
is more similar to the blue person?

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Or would you say that the purple person
is more similar to the red person?

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this is, a
this is more relevant for the,

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clustering, tasks or clustering

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algorithms that we'll be discussing
in, the following section of the course.

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But it is just such a simple illustrative
example that we're going to use it here.

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We're going to talk about it.

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We're about here
to show the importance of feature scaling.

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So once again, if you'd like to pause
this video please go ahead and try to see

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would you group the purple person
with the blue person,

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or would you group the purple person
with the red person?

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And now let's have a look at it together.

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So the let's look at the differences.

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The difference here in salary is $10,000.

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And here it is $8,000.

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And in terms of age,

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the difference between the purple
and the blue person is one year.

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And between the purple
and the red person is four years.

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Now, what can happen
with unscaled features?

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As we see here?

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is that the values, the unit values,

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of one column can be so much larger
than the other that it might overpower.

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So, for example, we can see that
the values of 10,008 thousand

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are much, much greater
than the values of one and four.

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So we might make the erroneous conclusion
that, okay, we're going to ignore values

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one four, because those are such small
differences compared to 10,000, 8000.

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We're going to focus on these large
of magnitude numbers 10,008 thousand.

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And out of them
we'll say that the purple person

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is clearly closer to the red person
because,

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that value is 8000.

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It's $2,000 less or 2000 units less than,

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the value, the difference
between the purple and the blue person.

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And as a result, we would group the purple
person with the red person.

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Now, we don't want

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this or similar things
happening in our algorithms.

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and that's why
we need to normalize variables,

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because we can't compare right now
when comparing salaries to years.

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It's it's like comparing apples
and oranges.

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These are not non comparable things.

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What if years was expressed
not in years but in minutes.

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Then those values would be much higher
or in seconds would be even higher.

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And even if you have the same units
of measurement

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like dollars and dollars into columns,
they still might not be comparable

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because they're relating
to different things.

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So it's important to scale your features.

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And so let's apply normalization
as a quick reminder.

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This is what the formula
for normalization is like.

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So we're going to apply it to the columns
one by one.

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So we are applying it to the dollar column
first after normal

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after normalizing 
our values will look like this.

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So let's go back for a second and go here.

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So I'll let you pause this video
if you'd like to do

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the manual calculations.

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This is, the result.

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And once we apply it to the first column,
our values will look like this.

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Once again, from here we end up here.

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And now we can compare
like for like based on this image,

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based on this data, which do you think
the purple person is closest to?

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Well, I think the answer is obvious.

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The purple

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person is almost right in the middle
between the red and the blue people.

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They're at 0.444, whereas in the H column

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the purple person is closest
to the blue person.

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It's very clear.

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So there we go.

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That's a quick illustrative example,
very simplistic but yet illustrative

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example of feature scaling.

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And I hope you enjoy seeing that together
for the lunch in the practical tours.

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On that note, I look forward
to seeing you back here next time.

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And until then, enjoy machine learning.