**Single Linkage**

The distance between two objects is defined to be the smallest distance
possible between them. If both objects are clusters, the distance between the
two closest members are used. This calculation is done by equation (8). Single
linkage often produces a very skewed hierarchy (called the chaining problem) and
is therefore not very useful for summarizing data. However, outlying objects are
easily identified by this method, as they will be the last to be merged.

**Complete Linkage**

This method is much like the single linkage, but instead of
using the minimum of the distances, we use the maximum. Complete linkage tends
to be less desirable when there is a considerable amount of noise present in the
data. Not surprisingly, complete linkage tends to produce very compact clusters.

**Average Linkage**

This method takes the mean between all the objects in cluster i
to all the objects in cluster j. There are several different ways of defining
the average distance. In literature some of these are referred to as WPGMA
(weighted pair group method with arithmetic mean), UPGMA (unweighted pair
group method with arithmetic mean), UPGMC (unweighted pair group method
centroid) and WPGMC (weighted pair group method centroid).