Done? While there’s not necessarily a “correct” answer here, it’s most likely you split the bugs into four clusters. The spiders in one cluster, the pair of snails in another, the butterflies and moth into one, and the trio of wasps and bees into one more.

That wasn’t too bad, was it? You could probably do the same with twice as many bugs, right? If you had a bit of time to spare — or a passion for entomology — you could probably even do this same with a hundred bugs.For a machine though, grouping ten objects into however many meaningful clusters is no small task, thanks to a mind-bending branch of maths called combinatorics, which tells us that are 115,975 different possible ways you could have grouped those ten insects together. Had there been twenty bugs, there would have been over fifty trillion possible ways of clustering them.

With a hundred bugs — there’d be many times more solutions than there are particles in the known universe. How many times more? By my calculation, approximately five hundred million billion billion times more. In fact, there are more than four million billion googol solutions (what’s a googol?). For just a hundred objects.Almost all of those solutions would be meaningless — yet from that unimaginable number of possible choices, you pretty quickly found one of the very few that clustered the bugs in a useful way.

Us humans take it for granted how good we are categorizing and making sense of large volumes of data pretty quickly. Whether it’s a paragraph of text, or images on a screen, or a sequence of objects — humans are generally fairly efficient at making sense of whatever data the world throws at us.Given that a key aspect of developing A.I. and Machine Learning is getting machines to quickly make sense of large sets of input data, what shortcuts are there available? Here, you can read about three clustering algorithms that can machines can use to quickly make sense of large datasets. This is by no means an exhaustive list — there are other algorithms out there — but they represent a good place to start!You’ll find for each a quick summary of when you might use them, a brief overview of how they work, and a more detailed, step-by-step worked example. I believe it helps to understand an algorithm by actually carrying out yourself. If you’re really keen, you’ll find the best way to do this is with pen and paper. Go ahead — nobody will judge!

There are several variations on the algorithm described here. The initial method of ‘seeding’ the clusters can be done in one of several ways. Here, we randomly assigned every player into a group, then calculated the group means. This causes the initial group means to tend towards being similar to one another, which ensures greater repeatability.

An alternative is to seed the clusters with just one player each, then start assigning players to the nearest cluster. The returned clusters are more sensitive to the initial seeding step, reducing repeatability in highly variable datasets. However, this approach may reduce the number of iterations required to complete the algorithm, as the groups will take less time to diverge.An obvious limitation to K-means clustering is that you have to provide a priori assumptions about how many clusters you’re expecting to find. There are methods to assess the fit of a particular set of clusters. For example, the Within-Cluster Sum-of-Squares is a measure of the variance within each cluster. The ‘better’ the clusters, the lower the overall WCSS.