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How could you automatically cluster the cities of a country, given only their positions and populations? I’ve animated one method, which works in a very simple manner. At step zero, it just randomly assigns each city to one of the clusters. At step 1, it calculates the centre of each of the clusters from the previous step, and reclassifies the cities by what centre they are closest to. At step 2, it does the same again. You can repeat this as much as you want! So you start with a random configuration, then keep refining it- always using the previous step to recalculate the model. See how it always converges to quite a nice clustering of the cities. This idea of starting somewhere random, and continually refining the model is how a lot of machine intelligence works; an analogous method could help you train a speech recogniser, for example. [Mathematica notebook] [more]

How could you automatically cluster the cities of a country, given only their positions and populations? I’ve animated one method, which works in a very simple manner. At step zero, it just randomly assigns each city to one of the clusters. At step 1, it calculates the centre of each of the clusters from the previous step, and reclassifies the cities by what centre they are closest to. At step 2, it does the same again. You can repeat this as much as you want! So you start with a random configuration, then keep refining it- always using the previous step to recalculate the model. See how it always converges to quite a nice clustering of the cities. This idea of starting somewhere random, and continually refining the model is how a lot of machine intelligence works; an analogous method could help you train a speech recogniser, for example. [Mathematica notebook] [more]

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Matt Henderson

I post original stuff about maths, space, computational linguistics and other things that I like. This blog is meant to be accessible and interesting to people of all backgrounds. My undergrad was maths in Cambridge, and I'm now starting research in Speech and Language technology. Email me at If you're new, check out this overview of my posts. All code posted is in Mathematica.

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