Final answer:
Hierarchical clustering involves different linkage methods like Ward's linkage, maximum or complete linkage, average linkage, and single linkage, each producing clusters with distinct characteristics. Ward's minimizes variance within clusters, maximum linkage focuses on the furthest distances, average linkage balances the two, and single linkage.
Step-by-step explanation:
Applying different linkage criteria in hierarchical clustering helps in understanding how the results vary based on the method used. The main aim of hierarchical clustering is to build a hierarchy of clusters that can help in analyzing the data.
With Ward's linkage, the aim is to minimize the variance within each cluster. Here, the results tend to create more balanced clusters, which can be more meaningful if the goal is to minimize within-cluster variation. Conversely, with maximum or complete linkage, the focus is on the distance between the furthest members of different clusters. This can result in tighter clusters, but can also sometimes generate outliers or small clusters that are very distant from others.
In average linkage, the average distance between all pairs of individuals in any two clusters is calculated. This creates a balance between single and complete linkage and is less sensitive to outliers than complete linkage. Lastly, single linkage clustering (also known as the nearest neighbor technique) considers only the shortest distance between clusters for merging, leading to a tendency for 'chain-like' structures. This method is highly sensitive to outliers and can lead to elongated clusters.