The hierarchical clustering algorithm is based on a dissimilarity measure between observations. A common measure, and what we will use, is Euclidean distance. Other distance measures are also available.

As the iterations continue, it is important to understand that in addition to the distance measure, we need to specify the linkage between the groups of observations. Different types of data will demand that you use different cluster linkages. As you experiment with the linkages, you may find that some create highly unbalanced numbers of observations in one or more clusters. For example, if you have 30 observations, one technique may create a cluster of just one observation, regardless of how many total clusters that you specify. In this situation, your judgment will likely be needed to select the most appropriate linkage as it relates to the data and business case.

The following table lists the types of common linkages, but note that there are others:

The output of hierarchical clustering will be a dendrogram, which is a tree-like diagram that shows the arrangement of the various clusters.

As we will see, it can often be difficult to identify a clear-cut breakpoint in the selection of the number of clusters. Once again, your decision should be iterative in nature and focused on the context of the business decision.