Interesting Type of Chart: Hexagonal Binning

Author: Capri Granville

This chart communicates the same insights as a contour plot. What is interesting is the choice of hexagonal buckets (rather than squares) to aggregate data. In fact, any tessellation would work, in particular Voronoi tessellations.

3-D Voronoi tessellation 

The reason for using hexagons is that it is still pretty simple, and when you rotate the chart by 60 degrees (or a multiple of 60 degrees) you still get the same visualization.¬† For squares, rotations of 60 degrees don’t work, only multiples of 90 degrees work. Is it possible to find a tessellation such that smaller rotations, say 45 or 30 degrees, leave the chart unchanged? The answer is no. Octogonal tessellations don’t really exist, so the hexagon is an optimum.¬†

Hexagonal binning plots (source: here)

Implementation in R

The three plots described here (Voronoi diagram, hexagonal binning and contour plots) are available in the ggplot2 package.

  • Hexagonal binning: ggplot function with the parameter stat_binhex, see here
  • Contour plot: ggplot function with the parameters geom_density2 or stat_contour, see here ¬†(also works with contour)
  • Voronoi diagram: ggplot with the parameter geom_segment, see here

Applications

Voronoi diagrams can be used for nearest neighbor clustering or density estimation, the density estimate attached to a point being proportional to the inverse of the area of the Voronoi polygon containing it.

Example of contour map (source: here)

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