People need to learn to use standardized measures for things.
So take me for example when I drive anywhere,
I drive in miles, I drive in miles per hour.
My fuel economy is messaging miles per gallon,
but of course, I don’t pump fuel in gallons,
I pump it in liters.
And then but when I run anywhere so short distances
I run in kilometers and I run in kilometers per hour.
So I’m using two different systems there.
And any short distances I’m measuring are going to be in meters, not feet, right.
So if I’m measuring let’s say
around my house for painting,
I’m going to measure in square meters,
so I know how much paint to buy.
But then I’m selling a house, or I’m buying a house
I’m going to be looking at the size of the house in square feet.
Again, what, who knows why, British people.
If I’m baking anything,
it’s going to be weight in grams or kilograms going into the recipe.
But if I’m weighing myself is going to be in stones and pounds.
But of course a ton would for me would be a metric ton
但当然 对我来说 吨是公制吨
not an imperial ton.
And as I said, I measure fuel in liters
and most of my liquids are measured in liters
except for cause for beer and milk, which are in pints.
So this is the kind of problem you’re going to be dealing with
when you’re looking at data.
You’re trying to transform your data into a usable form.
Maybe the data is coming from different sources,
none of it goes together.
You need standardized units standardized scales,
so we can go on and analyze it.
<04 - 数据转换>
So let’s think back, we
what we’re doing is we’re trying to prepare our data
into a densest, most clean format
modeling or machine learning
or some kind of statistical test
to work out what’s going on and draw knowledge from our data.
So this is going to be an iterative process,
we’re going to be cleaning the data,
we’re going to transform the data
and then we’re going to reduce for data,
and transforming data is what we’re going to do today.
So let’s imagine that you’ve cleaned your data.
So we’ve got rid of as many missing variables as possible,
hopefully all of them with deleted instances and attributes that
just we’re not going to work out for us.
Now what we’re going to try and do
is we’re going to try and transform our data
so that everything’s on the same scale
Everything makes sense together
and if we’re bringing datasets from different places,
we need to also make sure all the units are the same
and everything makes sense.
There’s no point in trying to use machine learning
or sum or clustering or any other mechanism
to draw knowledge from our data if our data is is all wrong.
So today we’re going to be looking at census data.
Now census data is kind of a classic example of a kind of data
you might look at in data analysis.
It has got lots of different kinds of attributes,
things that are going to need cleaning up and transforming.
So we’re back in our we’re going to read the census data
using census is read CSV
输入> census <-read.csv(''census.csv)
So we’ve downloaded some census data that
represents samples from the US population to begin with.
We’re going to read that in and you can see that
we’ve got 32,000 observations and 15 attributes
So what are the first math.
So let’s have a quick look at just a little bit of it
and we can see the kind of thing we’re looking at.
So we’re going to say head of census
and that’s just going to produce the first few rows
so we can kind of see the kind of data.
So you can see we’ve got age
we’ve got what working classification that person has, their educational level
and numerical representation about whether they’re married or not this kind of thing
So there’s a lot of different kinds of data here
some of it is going to be nominal
So for example, this working-class
state government, private employee.
That’s a nominal value.
We might have ordinal values or ratio values
or interval values
We’re gonna have to delve into a little bit closer to find out what these are.
Now what we do to transform this data
into a usable format for clustering or machine learning
is going to depend on exactly what these types of these columns are
and what we want to do with them
So let’s look at it just a couple of the attributes
and see what we can do with them, right?
We’re going to use a process called codification.
The idea is that maybe things like random forests or
multi-layer perceptrons, you know neural networks
aren’t going to be very amenable to putting in text-based inputs.
So what we want to do is try and replace these attributes
with a numerical score.
All right. So let’s look at just for example of a working class,
好吧 接下来看一些例子 比如工作类型
and also for example the educational level. So education.
Now work class is the kind of class of worker that we’re looking at here
So for example a state worker or in private sector,
or someone that worked in a school or something like this.
Now this is a nominal value.
That means there’s no order to this data at all
we can’t say but someone in state is higher or lower than someone in private
and we can’t also say but let’s say state is two times more or less than some other one.
That makes no sense at all. Alright.
So what we can we can replace this with numbers.
so let’s say we could replace private with zero
and state with one
and you know, self-employed with two and so on, right
And that we’ve got back perfectly reasonable thing to do,
but it’s still nominal data.
So what we can’t do is then calculate a mean and
say “ah the mean is halfway between private and public”
that doesn’t make any sense.
Just because something has been replaced by a numerical score
doesn’t mean that it actually represents something that we can quantify in that way, right?
It’s still nominal data.
Okay, so I bet the best advice I can give is
feel free to codify your data into easy-to-read numbers
but just bear in mind that
you can calculate the mode just like you know the most common,
but you can’t calculate the median and you can’t calculate the mean.
Another example would be something like the educational level.
Now theoretically this is ordinal data,
so we could save it someone with a an undergraduate degree
is maybe slightly higher in terms of their the amount of time they spent in education,
than someone with a high school diploma.
But we don’t know exactly what the distance is,
and what’s the distance between let’s say a high school and a degree and then a PhD,
即我们无法算出拥有高中 本科 博士
and so on an MD and things like this.
We can represent these using numbers,
and probably in order, right,
so we could say that zero is no education
and one is sort of the end of primary school
and two is the end of high school and so on and so forth
it’s difficult to calculate distances between these things
We don’t know what high school is two times more than primary school
and half of a degree or something like that.
That doesn’t really make sense.
you might be able to calculate a median on this or a mode,
but you can’t calculate an average.
You can’t say the average level of education
is halfway between high school and undergraduate.
That doesn’t make any sense either.
So for any kind of attribute that is nominal or
possibly ordinal and it’s sort of represented using text
we can codify this so that it’s more amenable to things like
decision trees depending on the library you’re using, right?
But you just have to be careful all machine learning algorithms
will take any number you give them
and you just have to be careful that this makes sense to do.
So what you would do is you would go through your data
and you’d begin to systematically replace appropriate attributes
with numerical versions of themselves,
remembering all the time,
that they don’t necessarily represent true numbers,
you know in a ratio or interval format.
So for any text-based value,
we’re going to start with replacing possibly with numerical scores.
What about the numerical values?
Well, they might be okay,
but the issue is going to be one of scale.
you might find for example in this census data
that one of the dimensions
or one of the attributes is much much larger than another one.
So for example, this dataset has hours per week
which is obviously going to be somewhere between naught and maybe 60 or 70 hours
for someone has got, you know a very strong work ethic,
and salary, right?
Or salary or income or any other measure of, you know, monetary gain.
Now obviously hours per week is going to be in the tens and
Salary could be into the tens of thousands. Maybe even the hundreds of thousands
Those scales are not even close to being the same.
That means if you’re doing clustering or machine learning
on this kind of data
you’re going to be finding the salary
is kind of overbearing everything, right
So it’s going to be very easy for your clustering
to find differences in salary,
and it’s harder for it to spot differences in hours,
because they’re so small in comparison, right?
So we need to start to bring everything onto the same scale.
The more attributes you have
which is another way of saying, the more dimensions you have to your data,
then the further everything is going to be spread around.
If we can scale all of these values to between
sort of let’s say around 0 and 1,
then everything gets more tightly sort of controlled in the middle,
And so it gets much easier to do clustering
or machine learning or any kind of analysis we want.
So let’s look back at our data
and see what we can do to try and scale some of this into the right range.
So we’re going to look back at the head of our data again
so our numerical values are things like the capital gain
the capital loss which I guess
presumably how much money they’ve made in the loss that year,
probably for normalize them on some scale
and then things like the hours per week that they work.
and their salary which at this case is greater than or less than 50,000.
So let’s have a quick look at the kind of range of values we’re looking at here
so we can see if scalings even necessary
Maybe we got lucky
and the person did it before they sent us the data
So we’re going to apply a function across all the columns
and we’re going to calculate the range of the data
So this is going to be apply on a census data
division 2, so that’s all of our columns,
and we’re going to use the range function for this,
and this is going to tell us okay,
so for example the age ranges from 17 to 90
the educational level from 1 to 16
It gives you the range for things like nominal values as well,
but they don’t really make any sense
I mean working class ranges from question mark to without pay,
you know is meaningless.
And then so for example capital gain ranges from zero to nearly one hundred thousand,
and capital loss from zero to four thousand.
And finally the hours per week ranges from 1 to 99,
So you can see that the capital gain
is many orders of magnitude larger in scale than the hours per week.
We’re going to need to try and scale this data.
We’ll begin by doing to make our lives a little bit easier.
It’s just focus on the numerical attributes right,
so we’d have to worry about the nominal values, which we’ve not codified yet
We’re going to select all the columns from the data where they are numeric.
So that’s this line here, and paste that down here.
So we’re going to s apply that applies over each of the fields is it numeric,
and that’s going to give us a logical list
that says true or false depending on whether those columns are numeric.
What we’re doing here is selecting from this list any bit of true
and then finding their names.
So what are the names of a columns for the numeric?
So let’s have a look at just a range of these attributes
to make our life a little bit easier.
So I’m gonna run this line
and so this is a simplified version of what I was just showing,
you can see that capital gain is massive
compared to the hours per week for example.
Let’s have a look at the standard deviation.
the call that the standard deviation, is the average distance from the mean,
so it kinda gives us an idea of the spread of some data, right.
Is it very tight and everyone owns roughly the same
or is it very spread out and it’s huge deviations.
And the answer is there’s pretty huge deviations.
So the age has a standard deviation of 13 so it, obviously
that means that most people are going to be kind of in the middle
and on average they’re going to be 13 years younger or older,
but you can see that things like capital gain have over 7,000 standard deviation,
which is a huge amount.
To give you some idea what we’re aiming for,
it’s very common to standardize this kind of data.
So the standard deviation is 1 right.
So, 7,000, much too big.
Let’s plot an example
to gives you some idea of what the kind of problem is when we have these massive ranges.
So I’m going to plot here a graph of age versus capital gains, right
We know age goes between about one and a hundred
and capital gain is much much larger.
So if I run this
basically the figure makes no sense at all,
because the capital gain ranges from zero to one hundred thousand
and as a few people earning right at the top scale,
everything is sort of squished down the bottom.
We can’t see anything that’s going on.
There’s no way of telling whether
the capital gain of an individual is related to their age.
I mean it probably is, right
Cause retired people, people who are very young,
perhaps earn slightly less.
We can’t really see that here,
because it’s just too compressed, right
We need to start trying to bring these things together
so that we can perform better analysis.
What we’re going to do is creating a new data frame
with just the numerical attribute.
so we want to focus on just to make our life a little bit easier
and then we’re going to write a normalized function to
move all our data to between 0 and 1,
and we will do this per attribute.
So for example, if you’ve got some data which goes between a minimum and a maximum
and we want to scale this data to between 0 and 1
All we need to do is first of all, take away the minimum,
and that’s going to move everything to be
from 0, to max minus min.
And then we’re going to divide by this distance here,
so this is max minus min.
And if we divide by this everything is going to go from 0 to 1.
So that’s exactly what we’re doing in this function here
we’re gonna function X
and it subtracts the minimum of X
and then divides by the difference between the maximum and the minimum alright.
So this is very standard. So I’m going to run this.
I’ll let you write functions like this and then use them
in applications over data.
So we’re going to calculate a normalized census dataset,
which is we’re going to apply over dimension to
this normalized function we just wrote.
And then now if we look at the range will see that our range is now
between 0 and 1 for all of our data, which is exactly what we want.
The normalization is a perfectly good way of handling your data.
If everything is between 0 and 1
we have fewer problems with the scale of things being way off right.
Now some statistical techniques like PCA
that we’re going to talk about in another video
They require standardized data,
that’s data is centered around zero,
has a mean of zero and a standard deviation of one.
Now we can standardize data pretty easily in the same way.
Actually, we don’t need to write our own function for this,
the scale function in R performs this for us.
So we’re going to take the census data over numerical attributes
and we’re going to call the scale function
and that’s going to take all of the attributes
and center them around their mean,
so that means the mean will become close to zero
and it’s going to divide them all by the standard deviation
so their standard deviation becomes one.
So if we run that and then we have a look at the mean of this data
So for example here, we calculate the mean.
You can see that I mean these values are very very close to one
That’s 10 to the minus 17 or something like that, very very small.
And if we look at the standard deviation, and similarly, they’re all going to be 1.
Alright, so this is now standardized data.
This is a very good thing to do
if you want to use your data in some kind of machine learning algorithm or some kind of clustering.
Let’s imagine now that we want to join some datasets together.
So we standardize data everything’s between 0 and 1,
or it’s centered around 0 with a standard deviation of 1,
we’ve codified some attributes.
What happens if we get other data from other sources？
You can imagine that census data from the US might be a bit useful.
But maybe we want census data from Spain
or from the UK or from another country.
Can we join all of these together
to get a bigger more useful dataset? Alright.
Now the thing to think about when you’re doing this,
is just to make sure that everything makes sense, right?
Are the scales the same?
Are they all normalized or none of them normalized?
Because otherwise, what you’re going to be doing is you’re going to be adding, you know,
pay between naught and a hundred thousand, to somewhere between naught and one,
nothing makes any sense anymore.
You’re gonna wreck your data.
So let’s have a look at this on the census dataset.
We have some Spanish census data in a very similar format
to our census data from the United States.
Let’s have a quick look.
So I’m going to read the CSV file of Spain data.
Let’s remind ourselves of the columns that we had in our census data from the United States.
These are the numerical columns,
so we have age, education number
capital gain capital loss this kind of thing.
Let’s look at the Spanish dataset
to see if we can just join the two together.
So I’m gonna run head Spain,
that’s going to give us the first few rows
and you can see that
there’s some of the stuff in there is as it was before
so things like what their level of education is,
whether they work in the private sector or the public sector, right.
We’re going to need to remove these things
to create just a numerical attributes.
And the other problem is if you look carefully,
you’ll see that the capital gain in the Spanish dataset is in euros,
not in dollars, right.
Now that’s a huge problem.
They don’t they’re not massively different obviously
they’re on the same order of magnitude
But we don’t want to be jamming
capital gain in euros next to dollars
because those two scales are not the same, right?
So what we need to do first
is scale this data using some kind of exchange rate.
So here what we’re going to do is we’re going to create a new column in Spain
so given a Spain data frame,
we’re going to say the Spain capital gain is equal to the
Euro capital gain times by 1.13,
which is the exchange rate we’re going to use.
Now It’s quite important in this kind of situation
not just to look up the exchange rate online.
You’ve got to consider but this might have been collected a while ago
What was the exchange rate when this data was collected right,
these are things you’re going to have to think about.
So let’s run that line,
and let’s do the same thing for the capital loss.
Now we’re going to keep just the numerical attributes of
our census data and of the Spanish data,
and we’re also going to add another column,
that is what country they come from,
otherwise we’re not going to know.
So we’re going to use the columbine function
to combine the census data as numerical attributes
and the native country which in this case will be the United States.
We’re going to do the exact same thing for the Spain data,
which will be basically exactly the same
except obviously we’re also going to have Spain as the native country.
And then we’re going to use the rowbind feature
to just join those two tables together
Now that will only work if those two datasets have the exact same attributes.
‘nu_census’ is not found.
What did I do wrong?
So I had a typo.
So let’s join these two together using rbind.
There we go. And so our United dataset now has
the combined observations for the United States and Spain.
Now, what you wouldn’t want to do is just join them together
and just leave it at that, right.
You want to perhaps have a little look at some plots to make sure that
the distributions of the data you’ve just joined together make sense.
For example, alright,
the United States data has a nice broad distribution of different ages.
We want to make sure that the Spanish data has that same distribution
Otherwise, you’re kind of going to skew your dataset.
So, for example, let’s have a look at roughly whether the levels of capital gain
are approximately the same for both the United States and the Spanish dataset.
So I’m gonna use ggplot for this. We’re gonna plot a bar chart
where we’ve color-coded United States and Spain,
and you can see that broadly speaking
there’s a lot in the kind of around zero or less than 50k,
and then there’s a few a little bit above.
Alright, so that looks broadly speaking the same distribution.
I’m fairly happy with that.
This is gonna be a judgement call
when you get your own data.
So I’ll clear the screen
and then let’s have a look at the next plot.
So the next plot is going to be capital loss versus the native country.
Let’s make sure those distributions are the same.
So it’s posting there and broadly speaking again yes,
the majority are down the bottom,
and then there’s a few United States ones
and a couple of Spanish ones up at the top as well.
Again, it’s not a disaster.
That’s probably ok.
Finally, let’s have a look at ages by native country.
So if we plot this,
we can see two very very similar distributions.
You can see that it’s essentially a bell curve.
Maybe slightly skewed towards older participants
for the United States and very very similar for Spain. This is okay.
If we hypothesized that
capital gain, capital loss and salary
was something to do with your age,
then it would make sense to have two datasets that you’re joining together
have very similar distributions in this regard.
So let’s look at one more dataset from Denmark.
Alright, so it’s the same thing, same format.
We’re gonna read the CSV,
and we’re going to have a look at just the top few rows to make sure it’s in the same format,
so that’s using a head function,
and you can see actually we’ve already removed the nominal
and other text attributes from here
and we’ve just got the numerical ones.
And actually also capital gain and capital loss
are already in dollars in this dataset
so we don’t have to perform a conversion.
So we can use rbind to put these two things together,
and now we just need to check the distributions are the same.
we’re going to put the age against the native country,
and see if these towards the same distributions.
And you actually you can see this isn’t looking too good.
The United States and the Spanish datasets
have very similar distributions.
The participants or the people who have been polled from Denmark are much much older on average, right?
This could have an effect on things like capital gain,
so I wouldn’t necessarily feel comfortable just joining this dataset in,
without you thinking about it a little bit more closely.
whenever you’re joining dataset like this taking data from different sources,
think carefully, to make sure that it’s fair
and what you are doing is a reasonable, concatenation of datasets.
And actually these are the features
that power Spotify recommender system and numerous others.
So we’ve got things like acousticness.
How acoustic does it sound from
from a zero to a one?
We’ve got instrumentalness.
I’m not convinced that’s a word.
That, how, how, to what extent is it speech or not speech, alright.
And then things like tempo…
People need to learn to use standardized measures for things.