The Joy of Hex

1. The Joy of Hex: Challenges in creating and interpreting spatial bins Sarah Battersby | Daniel Strebe | Michael Finn

2. The big picture Lots of data, not a lot of pattern 156,138,722 taxi pick up locations

3. Simplify - Aggregate 156,138,722 points vs. A few hundred bins Easy to create Nice, regular pattern Tricky to make useful

4. Or…

5. Let’s dig into the challenges… What to think about when you want to think about how people think about spatial bins…

6. A first decision – bin shape

7. Option 1 Simple relationship side to area Quick and easy for aggregation But… Strong and distracting horizontal / vertical lines Potential artefacts with linear cultural features like roads

8. Subdivides nicely Option 1

9. Minimizes edge effects & linear patterns More compact shape is ‘pleasing’ But… More complex relationship of side to area Spacing more irregular A little more challenging to aggregate points Option 2

10. Also loses the nice subdivision Option 2

11. But… they are ‘edgier’ and people like them (maybe too much) Source: http://indiemaps.github.io/hexbin-js/tests/walmart.html

12. Short story on bin shape? Whatever works for you your data your workflow your hipness quotient

13. Second big decision… What do your readers need to do? Value for individual location General patterns Comparisons across maps

14. Value for individual location / general patterns Are your bins really the same size? Same shape?

15. Value for individual location / general patterns Are your bins really the same size? Same shape? On the plane? What projection are you using? Equal area projection

16. Value for individual location / general patterns Are your bins really the same size? Same shape? On the WEB MAP plane? 1. Regular bins in Web Mercator space

17. Value for individual location / general patterns Are your bins really the same size? Same shape? On the WEB MAP plane? 2. “Regular” bins in “spherical space”

20. Value for individual location / general patterns Image source: https://www.mapbox.com/blog/heat maps-and-grids-with-turf/ Are your bins really the same size? Same shape? On the WEB MAP plane? 2. “Regular” bins in “spherical space”

21. Value for individual location / general patterns But can’t I just bin on the sphere and save myself the headache? On the sphere? Can’t preserve both areas and angles …and perfect tessellation is a pain Hexagonal tiling with 12 pentagons (the soccer ball problem)

22. A take home message Be cautious with how your bins are created / measured Understand the parameters in the API Even if they are just “graphics” and the exact bin area doesn’t matter… …it’s important to know how they were made

23. Comparison across maps Multiple hexbin maps? Be careful with the alignment / origin of your bins Grid of bins – based on specified origin Bins to compare – same spatial location

24. Comparison across maps Multiple hexbin maps? Be careful with the alignment / origin of your bins Grid of bins – based on data extent Bins to compare – different spatial location Impossible to match aggregation

25. A take home message Not all tools for generating spatial bins allow for control of origin / placement So, if you want to make valid comparisons of binned data be careful…

26. Which brings up a bigger problem… Modifiable areal unit problem Change in size, shape, placement, etc. may give a different spatial pattern

27. (MAUP video)

28. And an interesting question What is it that people are going to interpret anyway? When we encode spatial bins, do people see density or count? Do they assume that it is just a graphical, planar density? Or is it assumed to be spherical density? Or do they expect it to be both count and correct generic density? Planar = Spherical

29. Map shows aggregation on plane: Bins with same count

30. Bins with different count

31. A take home message We need to understand what people really see in binned visualizations to figure out how best to visualize it My thought on naïve understanding is an assumption of both count and density, so we have a big problem with projections…

32. One last point… Irregular bins to preserve area But we lose benefit of bin regularity Computational (point in polygon) Visual …or “don’t do this if your geographic area is larger than {insert bounding box}”

33. But how do I know what that bounding box is??

34. What in the world was that mathematical scribble? Calculating the ‘Safe Zone’ to bin in projected space, and many other goodies can be found in… “Shapes on a Plane: Evaluating the impact of projection distortion on spatial binning” Download from: http://research.tableau.com

35. Questions? Sarah Battersby – sbattersby@tableau.com daan Strebe – dstrebe@tableau.com Michael Finn – mfinn@usgs.gov