From our similarity function, we could simply rank the results for each user, returning the most similar user as a recommendation—as we did with our product recommendations. Instead, we might want to find clusters of users that are all similar to each other. We could advise these users to start a group, create advertising targeting this segment, or even just use those clusters to do the recommendations themselves.

Finding these clusters of similar users is a task called cluster analysis. It is a difficult task, with complications that classification tasks do not typically have. For example, evaluating classification results is relatively easy—we compare our results to the ground truth (from our training set) and see what percentage we got right. With cluster analysis, though, there isn't typically a ground truth. Evaluation usually comes down to seeing if the clusters make sense, based on some preconceived notion we have of what the cluster should look like. Another complication...