Skip to main content
Mathematica

Return to Question

edited title
Link
kjo
kjo
  • 11.8k
  • 1
  • 33
  • 91

How: 2D scatterplots with quantitative density-dependent coloring (e.g. flow cytometry plots)

Tweeted twitter.com/#!/StackMma/status/608329389470793728
Source Link
kjo
kjo
  • 11.8k
  • 1
  • 33
  • 91

How: 2D scatterplots with quantitative density-dependent coloring (e.g. flow cytometry plots)

Consider the following scatterplot of a 50K-point dataset:

ListPlot[data,
 AspectRatio -> Automatic, PlotRange -> {{x0, x1}, {y0, y1}}, 
 ImageSize -> Small,
 Frame -> True, 
 FrameTicksStyle -> Directive[FontOpacity -> 0, FontSize -> 0]]

Mathematica graphics

The color quickly saturates as one moves from the edge of the distribution to its center. As a result, most of the density information is lost.

One can remedy this slightly by assigning an opacity below 1 to the points:

ListPlot[data,
 PlotStyle -> Opacity[0.05],
 AspectRatio -> Automatic, 
 PlotRange -> {{x0, x1}, {y0, y1}}, ImageSize -> Small,
 Frame -> True, 
 FrameTicksStyle -> Directive[FontOpacity -> 0, FontSize -> 0]]

Mathematica graphics

But this solution still has a couple of shortcomings:

  1. its dynamic range is still fairly narrow (even though it's wider than it was before); thus, most of the data cloud is still shows as saturated color;
  2. there's no explicit quantitative scale (e.g. a colorbar) tying colors (or in this case, shades) to densities;

The dynamic range problem could be solved by using more hues. This is what's routinely done when plotting flow cytometry data. For example:

enter image description here

(IMO, the plots in the last set would be improved if they included a color key, showing the correspondence between colors and densities.)

My question is how can I provide such quantitative density information in these scatterplots using Mathematica?