Whose Grid Map is better? Quality Metrics for Grid Map Layouts

Figure 1. Different US map layouts from six publishers. Visual encoding: Black border = invalid neighbors, Thick orange line = misdirection, Curve line = missing neighbors.

Quality metrics & Intuitions behind them

For these purposes, I have defined a set of metrics for evaluating the quality of a Grid Map layout. These following metrics can be used as guidelines for selecting a layout to use, or optimization goals for new layouts:

  1. Lookalike (Boolean): The overall shape looks similar to the geographic map. I prefer this to be a yes/no question than trying to come up with a number since it only helps with first impressions for viewers to recognize that it is a map of a certain geographical region, but does not affect the interpretation afterwards.
  2. Recall (%) : Regions that are neighbors in reality should appear as neighbors in the Grid Map. For example, North Dakota and South Dakota should be adjacent. A pair of regions that appear as neighbors in the grid map is considered valid if the two regions are really neighbors in a geographic map. A pair is considered invalid otherwise. Recall is computed from this formula:
    No. of valid neighbor pairs / No. of geographic neighbor pairs
  3. Inaccuracy (%) : Regions that are not neighbors should not appear as neighbors in the Grid Map. For example, California and Florida should not be next to each other.
    No. of invalid neighbor pairs / No. of neighbor pairs
  4. Misdirection (%) : The relative positions between neighbor regions should be close to reality. For example, North Dakota is on the north or South Dakota, so it should be on the north of South Dakota in the Grid Map. To compute this metric, an angle between the two regions in each valid neighbor pair is computed and compared against an angle between their centroids on a geographic map. If the difference is more than 45 degrees, it is considered a misdirection.
    No. of misdirections / No. of valid neighbor pairs
  5. Area: A good Grid Map should be compact. This is simply calculated from No. of Rows x No. of Columns

Case study

Six square tile grid map layouts from New York Times, NPR, Guardian, Washington Post, FiveThirtyEight and Bloomberg were selected for the study. (See Figure 1.) These were referenced by the NPR Blog. Of these six, FiveThirtyEight and Bloomberg excluded DC from their maps.

Figure 2. Neighbors — primary and secondary

Results

All of them, although look slightly different, pass the lookalike test, at least from my judgement. And as mentioned above, there is no point trying to compare which one looks more similar to the US. Let’s look at other metrics which are more interesting.

Figure 3. Recall, Inaccuracy and Misdirection
Figure 4. Area

Conclusions

Based on the results above, the New York Times’ version seems to perform best as it can capture most of relationships while also providing the least misleading visuals.

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Data Experience @airbnb / Prev: Turn data into pixels @twitter • Invent new vis @UofMaryland HCIL PhD • From @Thailand • http://kristw.yellowpigz.com

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Krist Wongsuphasawat

Krist Wongsuphasawat

Data Experience @airbnb / Prev: Turn data into pixels @twitter • Invent new vis @UofMaryland HCIL PhD • From @Thailand • http://kristw.yellowpigz.com