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

Hierarchical clustering is an agglomerative or bottom-up technique. By this, we mean that all observations are their own cluster. From there, the algorithm proceeds iteratively by searching all the pairwise points and finding the two clusters that are the most similar. So, after the first iteration, there are n-1 clusters and after the second iteration, there are n-2 clusters, and so forth.

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 datasets will demand that you use different cluster linkages. As you experiment with the linkages, you may find that some may create highly unbalanced numbers of observations in one or more clusters...