Natural Breaks Results Difference in Different GIS Analyst Tools

Question

I calculated natural break clustering in each GIS software and Python Jenkspy library.

The data is population of each city in Europe and this is the result below.

Jenkspy library and QGIS shows somewhat similar results (but not really) while other trials return totally different results.

I am going to try with CartoDB PostGIS Extension though, I am already doubting the result.

the input data is all same and I made 6 classes for division. But I am not understanding why the results are different.

Does anyone know the reasons?

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Surprisingly, QGIS 2.18 and QGIS 3 gave me different results with same data.

Answer 1

The first question to investigate is, what method are these programs using to calculate Natural Breaks? Are they all using the same method?

• QGIS calculates Natural Breaks (Jenks).
• Based on the name "Jenkspy" I assume Python Jenkspy also uses Jenks optimization.
• ArcGIS calculates Natural Breaks (Jenks).
• Geoda natural breaks maps "follow the pathbreaking work of Fisher(1958) and Jenks(1977)"

So it seems that all four programs use Jenks natural breaks optimization. What's not yet answered (but you can probably find this out if you dig further into the documentation for each program) is if they use exactly the same method, or if they each use their own method based on Jenk's optimization. For example, maybe Geoda uses a combination of Jenks optimization and Fisher's discriminant analysis.

The Jenks optimization method... is a data clustering method designed to determine the best arrangement of values into different classes. (source)

Jenks natural breaks optimization can be done in one of two ways.

1. The first way is an iterative process. It creates class breaks (possibly arbitrarily, possibly by some other method), calculates the "sum of the squared deviations from the class means," checks the result against "a minimal value," and if it doesn't meet that "minimal value," it repeats the steps and checks again. This goes on until the minimal value is met.
2. The second way is to calculate all the possible combinations of class breaks, calculate "sum of the squared deviations from the class means" for all combinations, and pick the combination with the lowest value.

To summarize:

• All four programs use Jenks optimization, but there's a lot of variation in how this method can be applied, leading to different results.
• You can test which program has the "best" method. Calculate the "sum of the squared deviations from the class means" for the class breaks created by each program. Whichever program has the lowest value, is getting the closest to optimal results.