Introduction to Hierarchical Clustering Methods

Difference between HC and other clustering methods

Unlike partitional methods, HC methods don’t aim to output a single partitioning of the data. Their goal is to construct a tree, called the cluster dendrogram, denoting how data can be merged or split into nesting clusters. See the figure below for an example tree. In a dendrogram, the x-axis displays all data points, the y-axis captures the distance measure of clusters being split or merged (that is, the height of the tree), and the tree structure shows how data can split/merge to form smaller/bigger clusters.

To construct this dendrogram, there are two approaches:

• Bottom-up: Each individual data point starts out as a cluster on its own (that is, as the leaves of the tree), then subsequently these clusters are merged to form bigger clusters at parent nodes. The root node contains the whole dataset. Algorithms using the bottom-up approach are called Agglomerative Hierarchical Clustering (AHC).
• Top-down: The whole dataset is assigned to a single cluster initially at the root node, then split out to smaller clusters until each cluster comprises a single data point. Algorithms using the top-down approach are called Divisive Hierarchical Clustering (DHC).