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So in our previous discussions, we've been focusing on the relationship

between data points, where we're plotting the data points as points.

In some cases, you want to display more than just points, you want to display

shapes to represent the data, and in that case you want to pack the shapes together.

So here's an example called a word cloud, and this is basically the overview

text from our data visualization course from the Coursera page.

And I've just passed this through a web page called Wordle.net and

it created this word cloud which basically displays the most common words,

the words that are distinctive that aren't everyday words like the, and and.

And words that are used multiple times get displayed larger than

the words that are smaller.

And then there's a process that packs these words into a collection,

so instead of just displaying the words in order horizontally

that you might see in a tag cloud, this word cloud is packed together.

And there is a spiral algorithm that it uses

to basically find a first open space to pack a new word in it.

Tries to start with the largest words first and then packs in the small ones

later based on that same spiral trial and error techniques spiraling out from

the middle to try to pack the words into the location that they'll fit into first.

And so these techniques tend to use area as a measure, and

we've looked at area as a measure before.

It's a pretty good quantitative measure, but ordinal, it's not very good.

Being able to tell whether two different shapes have the same area can be quite

difficult.

So if you have consistent shapes.

It's hard to tell if I have the same amount of area in the blue circle as in

this orange square.

But if you have consistent shapes, if I have two circles,

then I can tell that the areas are the same based on the length.

And then if the shapes are aligned, if they share the same base,

then I can just look at the height at the position, at the top and

tell if the orange circle is less than the blue circle in area.

And so area is very difficult to determine, especially

when you have inconsistent shapes, but becomes useful if you have consistent and

aligned shapes, because then you're using actual length and position.

Also area, as the area increases or decreases,

the length is going to increase or decrease as the square root of the area,

and so that also complicates figuring out a quantitative difference between shapes.

And so, if we want to plot a bunch of data without any coordinates attached to it,

you could just pack the data together using, for example,

area to display the data.

So this is a Tableau plot of the population from our

WDI database, and you can see some of the larger

items are labeled if the label will fit in the region, but

here the area is basically indicating population, total number of people.

The area is proportional to the number of people.

And because these are all the same shape we can do a pretty good job of

finding an ordinal.

I can tell that China has more people than India.

India has more people than United States.

United States has more people than Brazi, and so on.

And so we get a good indication, at least an ordinal indication,

of the differences in population, and we don't need to use any other

coordinates because we're we're just comparing the areas to each other.

We're not plotting anything horizontally or vertically,

we're just using the horizontal and vertical axis to keep our shapes disjoint.

So another way of plotting things horizontally or

vertically is to display them on a map, and in this case,

we've distorted the map into a cartogram.

Here's an ordinary atlas of the world, and here's that same atlas

distorted based on population, so that the amount of distortion,

the area of the region is proportional to its population.

And you can see that certain regions have grown larger than they were before, and

certain regions have grown to be much smaller.

There's not very many people in Siberia, and so that's very small given it's area.

India and China have a lot of population,

high population density, and so their regions have grown much larger.

In Africa you can see that Nigeria has grown to be quite large.

And so this is a a way of indicating with area,

certain data that you would want to visualize.

Again, it's relative.

It would be difficult to tell ordinally if the there's more people in for

example, France or Germany, based on this display because the shapes are different,

and it's difficult to judge area relationships between different shapes,

but we can certainly tell that Germany is is roughly the same

shape it's just grown larger with a little bit of distortion than it was before.

And so that's the distinction we're trying to make with the cartogram.

So how do you create those cartograms?

Well you start, in this case, with a grid of density data.

And this is an old algorithm for doing this.

There's better techniques that are more sophisticated but

also much more complicated.

This is a nice way to do it.

If you just fill a grid in with density data such as your local

population density so within some unit area, what is the population density?

And so it could be heavily populated in this area and

lightly populated in these areas.

And so you create a grid like that of rectangular cells and

then you just scale each cell by that density value.

So the squares that have a population density

of one-half get shrunk by one-half in area.

So that's about 70% horizontally and vertically.

The areas that have population density one stay the same size, and

the areas that have larger population densities would grow proportionally, so

these squares would become twice as big, these squares become three times as big.

And then you can see that what we had as a grid before now becomes disconnected.

And so to reconnect it, we want to reconnect these corners to their average

of the four corners that shared that corner.

So we want to find a new point for

this corner equal to the average of these four previous corner points.

So we create a new set of grid vertices equal

to the average of the four grid vertices that shared them before.

Or three or two depending on, or one, if you're on the perimeter.

And so we create this new grid and this new grid is deformed.

And so based on this deformed grid We keep iterating that over and

over until we get a final deformed grid, and

then we look at the differences between the original grid points and

their new positions in the deformed grid that sets up a deformation.

It basically tells us what direction we should move data points.

Then, we take our shape vertices of the outline data of our original map and

deform them based on these arrows, and we can smoothly interpolate

these arrows if we need in between values in order to create the cartogram.

Its basically,

we take a vector graphics representation of our data of our map and then deform

the vertices based on this type of deformation to create the cartogram.

So another technique that might be better than a cartogram is the ordinary

choropleth, and we see choropleths all the time.

It's basically data that's plotted over regions of a map.

This is that same population data but

plotted inside the original outlines of our regions.

In here, population is Is just given by the saturation of the color,

and when we're looking at ordinal values,

basically we can see that China has more population than India does,

has more population than the U.S., which has more population than Brazil and so on.

So you get a better indication of the order of these things from a chloropleth

than you might with a cardogram because area is such a poor indicator order,

whereas density saturation hue, density being intensity of a color or

saturation in hue, are much better indicators of order.

So there's several techniques now for plotting data without using coordinate

data associated with the data for it's layout.

We're deriving coordinate data.

In these most recent examples we are using geographical data, where we have maybe

a region name, or a country name, and then we're deriving the actual coordinates of

that, perhaps an outline to fill in, or a location on a map to generate.

Or we're using some other packing or layout algorithm to distribute the data.

Those are all useful techniques in In the case where you've got data that you don't

want to use the explicit coordinates in the data as coordinates for their display.

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3.3.1. Packing

数据可视化

与讲师见面