If you’ve been to a library, you’ve seen clustering at work. The Dewey Decimal System is a form of clustering. Dewey came up with a system that would attach a number of increasing granularity and in doing so, revolutionized libraries.

This idea of categorizing data points, or books, into groups is useful for organizing information. We don’t know what specific category they should belong to, so we just want to split the books into a set of categories.

This type of problem is much different than what we’ve encountered before. All of the problems we have looked at thus far have attempted to figure out the best functional approximation to assign to a given data set and its labels. Now we are more concerned with the data itself, not the labels.

As you will see in this chapter, clustering has one downside, which is that it doesn’t lend itself to use as well as other algorithms. This is called the *impossibility theorem*.

In this chapter, we will talk about clustering in general as it applies to cohorts of users, and then introduce *K*-Means clustering and Expectation Maximization (EM) clustering. Finally, we’ll finish with an example about clustering jazz records into groups based on styles.

The Clustering algorithm is an unsupervised learning problem and is great for grouping data. It can present issues, though, with application to problems; that is, it suffers from the impossibility theorem.

Grouping people into cohorts (clusters) makes a lot ...

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