I have census data for census output areas. Each area is a geographical region. I would like to partition these areas into contiguous super-regions with similar properties.
For example, in each area I have employment broken down by industry, and I would like to find contiguous areas with similar industrial make-up.
These areas can be represented as a planar graph, which is easy to obtain from a topology of the output areas. Each edge in the graph can be weighted by some similarity score between the two adjoined nodes, (cosine similarity between proportions of employment by industry, for example).
Partitioning the areas into contiguous regions can be achieved by partitioning this graph, for example, by finding the minimum cut, and recursively finding the minimum cut of each subgraph until the desired level of granularity is achieved.
I've just come up with this procedure myself, but it's so basic that I can't believe it doesn't already exist under some other name.
I haven't been able to find any literature on it, but it's likely that I don't have the right terms to search for, and I'd like to avoid reinventing the wheel.
Does this category of geographical partitioning exist already?
- If so, what's it called, and where is the relevant literature?
- If it doesn't exist, are there any obvious reasons it would be a bad idea?
In the case of employment broken down by industry, cosine similarity seems like a sensible similarity score, because the proportions all sum to unity. Are there more suitable similarity scores or graph partitioning methods that I'm overlooking?
It has occurred to me that minimum-cut partitioning of the graph will probably not work, since the outlying areas will have a smaller degree than the innermost areas. As such, we'd expect this procedure to just eat away at the outskirts.