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High Density Scatter Plots

01 May, 2013 - 3 min read

I gave a talk this weekend where a small portion of it was devoted to visualization. In it, I mentioned that charting distributions is important, but that there are situations where a basic scatter plot won't work very well. I didn't do a very good job explaining situation where it isn't the best and possible solutions.

The Why

Let's consider a situation where we have a lot of overlapping points and how that looks with a basic scatter plot. All examples in this post will use R and its fantastic plotting library ggplot2.

First we need a sample of points that will have high density.

df <- data.frame(x=rnorm(1000, 0, 1), y=rnorm(1000, 0, 1))

A basic plot looks like the following:

library(ggplot2)
ggplot(df, aes(x=x, y=y)) + geom_point()

Basic Scatter Plot

It's fairly clear that there are a lot of points around (0,0)... but it's also clear that there's just a black blob around (0, 0). So what if we wanted to make that a bit more clear.

Jitter

On easy option is to use jittering. This is done (in ggplot2) by adding the jitter argument to the geom_point function.

ggplot(df, aes(x=x, y=y)) + geom_point(position = 'jitter')

Basic Jitter Plot

Cool story, bro... so what's the difference. Well here it's not really obvious due the extra high density, which immediately gets to why jitter isn't always a good option. That's because it attempts to slightly alter the position of the points to make it more spread out, but if there's too many points it doesn't do much. Jittering is probably best when you don't have a huge number of points and the exact location of those points isn't important.

Adding Alpha

Another option is to use alpha on the points... effectively making the points slightly transparent. This create a situation where higher density areas will appear darker.

ggplot(df, aes(x=x, y=y)) + geom_point(alpha = 0.4)

Basic Alpha Plot

This is certainly nicer than the jitter when a lot of points are present.

Contour Lines

Here's another option that doesn't mess with the display of the points themselves, but adds contour lines (like a map) that spells out the areas of high density.

ggplot(df, aes(x=x, y=y)) + geom_point() + geom_density2d()

Basic Contour Plot

It's pretty easy hear to figure out which area of the plot are of higher density via the contour lines. But there is one other option... and my personal favorite.

HexBins

We can draw a whole bunch of hexagons on our plot that will then be colored dependent on the density. This is particularly good for lots of data. The reason for this is that with a huge number of points... the individual importance of a single point goes down, but understanding the distribution is more important.

ggplot(df, aes(x=x, y=y)) + stat_binhex()

Basic HexBin Plot

Conclusion

There's clearly several ways to do this, and this list isn't exhaustive, it's more important to be able to justify the decision to use a particular plotting technique than a broad statement about which of the preceding methods is best.