Cover by Philipp K. Janert

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Chapter 13. Finding Clusters

THE TERM CLUSTERING REFERS TO THE PROCESS OF FINDING GROUPS OF POINTS WITHIN A DATA SET THAT ARE IN some way “lumped together.” It is also called unsupervised learning—unsupervised because we don’t know ahead of time where the clusters are located or what they look like. (This is in contrast to supervised learning or classification, where we attempt to assign data points to preexisting classes; see Chapter 18.)

I regard clustering as an exploratory method: a computer-assisted (or even computationally driven) approach to discovering structure in a data set. As an exploratory technique, it usually needs to be followed by a confirmatory analysis that validates the findings and makes them more precise.

Clustering is a lot of fun. It is a rich topic with a wide variety of different problems, as we will see in the next section, where we discuss the different kinds of cluster one may encounter. The topic also has a lot of intuitive appeal, and most clustering methods are rather straightforward. This allows for all sorts of ad hoc modifications and enhancements to accommodate the specific problem one is working on.

What Constitutes a Cluster?

Clustering is not a very rigorous field: there are precious few established results, rigorous theorems, or algorithmic guarantees. In fact, the whole notion of a “cluster” is not particularly well defined. Descriptions such as “groups of points that are similar” or “close to each other” are insufficient, because clusters must ...

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