NACIS 2016 Presentation Sarah Battersby, Tableau Software Complex, large N point datasets present challenges for visualization and synthesis of spatial patterns due to the density of marks and resulting clutter from overlapping mark symbols. One suggested method for dealing with complex point datasets is to partition the space into polygonal bins, and symbolize each bin based on point count inside the bin. Because regular polygonal (e.g., square or hexagonal) bins appear as same size and shape, they are suggested as a method for improving ability to analyze smooth, continuous change in point distributions, while avoiding artifacts from irregular political bin geometry. However, there is a fallacy if regular geographic bins are really considered to represent "same size and shape." In this presentation, we discuss challenges and tradeoffs the cartographer must consider in creating spatial bins, and, more importantly, challenges the map reader faces in interpreting bins in a way that aligns with the cartographer’s intended message.

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”

18. 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”

19. 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