Clustering spatially connected polygons so all clusters have approximately the same size

Wrangling Polygons: How to Make Spatial Clusters That Are Actually Useful (and Equal!)

Okay, let’s talk maps. Not just pretty pictures, but the kind of maps that do something. Specifically, how do you group those funky polygon shapes on a map – think counties, neighborhoods, forest patches – into clusters that are connected and, crucially, roughly the same size? Turns out, it’s a surprisingly tricky problem, and one that pops up way more often than you’d think.

We’re not just talking about drawing lines on a map. This is about creating meaningful regions. You see, most clustering algorithms are designed for points scattered in space. Polygons? They throw a wrench in the works. You’ve got to consider how they touch, share borders, and whether they form cohesive chunks. And then, to add insult to injury, you need those chunks to be about the same size. It’s like herding cats, but with GIS data.

So, why bother with all this spatial gymnastics? Well, imagine you’re redrawing sales territories. You wouldn’t want one salesperson covering a tiny, densely populated area while another is stuck with a vast, sparsely populated one, right? You want fairness, balance. Or picture dividing a forest for conservation efforts. You want contiguous zones, not scattered fragments, and you want each zone to be manageable. That’s where spatially constrained clustering comes in – it ensures your clusters are geographically sound and relatively equal.

Now, let’s dive into the toolbox. What algorithms can help us tame these polygons?

First up, we have Spatially Constrained Hierarchical Clustering (SCHC). Think of it as building clusters from the ground up, always making sure that everything sticks together geographically. Algorithms like SKATER and REDCAP fall into this category. SKATER, for instance, builds a kind of skeletal structure connecting neighboring polygons and then snips it apart in strategic places to form clusters. REDCAP is another family of methods that uses dynamically constrained agglomerative clustering and partitioning.

Then there’s Constrained K-Means Clustering. K-means is a classic clustering algorithm, but it needs a little help to deal with spatial data. This variation uses graph theory to find those optimal clusters, ensuring each one has a minimum number of polygons. I’ve even seen folks whip up Python scripts in QGIS to make this happen. Pretty cool, huh?

Don’t forget DBSCAN (Density-Based Spatial Clustering of Applications with Noise). The original DBSCAN isn’t perfect for our equal-size quest, but tweaked versions, like P-DBSCAN, can do a solid job of grouping polygons based on their spatial relationships.

ArcGIS Pro users, take note! There’s a Spatially Constrained Multivariate Clustering tool that’s worth checking out. It uses the SKATER algorithm to find those natural clusters based on attributes and size limits.

Finally, for those who like a hands-on approach, there’s the “Make One Group” Algorithm. It’s pretty much what it sounds like: you grab a polygon, add its neighbors, and keep going until you hit your target size. It’s a bit more manual, but it gives you a lot of control.

Of course, there are trade-offs. Sometimes, forcing spatial contiguity means grouping polygons that aren’t all that similar in terms of their attributes. You also have to decide exactly what “spatial relationship” means – does sharing a corner count? And let’s be real, some of these algorithms can be computationally heavy, especially with massive datasets. Plus, you might end up with clusters that look a bit…blobby. And Constrained K-means might get stuck sometimes.

But when it all comes together, the results can be powerful. Think about those sales territories again, or planning fiber optic networks, or allocating resources across a region. Even redrawing political districts to ensure fair representation! These are all real-world problems that can be tackled with the right spatially constrained clustering approach.

So, there you have it. Clustering polygons into equal-sized, contiguous groups isn’t always easy, but it’s a skill worth having in your spatial analysis toolkit. Experiment with different algorithms, understand their quirks, and get ready to wrangle those polygons into submission!