Agglomerative clustering

In contrast to algorithms, such as k-means, where the dataset is partitioned into individual groups, agglomerative or hierarchical clustering techniques start by considering each datapoint as its own cluster and merging them together into larger groups from the bottom up (Maimon, Oded, and Lior Rokach, eds. Data mining and knowledge discovery handbook. Vol. 2. New York: Springer, 2005). The classical application of this idea is in phylogenetic trees in evolution, where common ancestors connect individual organisms. Indeed, these methods organize the data into tree diagrams, known as dendrograms, which visualize how the data is sequentially merged into larger groups.

The basic steps of an agglomerative algorithm are (diagrammed visually in the figure below):

1. Start with each point in its own cluster.
2. Compare each pair of datapoints using a distance metric. This could be any of the methods discussed above.
3. Use a linkage criterion to merge datapoints (at the first stage...