A hierarchical clustering is a sequence of partitions in which each partition is nested into the next partition in the sequence. An agglomerative algorithm for hierarchical clustering starts with the disjoint clustering, which places each of the n objects in an individual cluster.
The clustering algorithm being employed dictates how the proximity matrix should be interpreted to merge two or more of these trivial clusters, thus nesting the trivial clustering into a second portion.
The process is repeated to form a sequence of nested clusterings in which the number of clusters decreases as the sequence progresses until a single cluster containing all n objects, called the conjoint clustering, remains.
A divisive algorithm performs the task in the reverse order.
Two specific hierarchical clustering methods are now defined called the single- link and the complete-link methods.