Differente Types of Clusterings

An entire collection of clusters is commonly refered to as a clustering, and in this section, we distinguis various types of clusterings: hierarchical (nested) versus partitional (unnested), exclusive versus overlapping versus fuzzy, and complete versus partial.
hierarchical versus Partitional
The most commonly discussed distinction among different types of clustering is whether the set of clusters nested or unnested, or in more traditional terminology, hierarchical or partitional. A partitional clustering is simply a division of the set of data objects into non-overlapping subsets (clusters) such that each data objects is in exactly one subset. Taken individually, each collection of clusters is a partitional clustering.
If we permit clusters to have subclusters, then we obtain a hierarchical clustering, which is a set of nested cluesters that are organized as tree. 
Each node (cluster) in the tree (except for the lead nodes) is the union of its children (subclusters), and the root of the tree is the cluster containing all the objects. Often, but not always, the leaves of the tree are singleton clusters of individual data objects. If we allow clusters to be nested, then one interpretation, is that it has two subclusters, each of wich, in tun, has three subclusters. The clusters shown, when taken in that order, also form a hierarchical (nested) cluestering with, respectively.
Finally , note that a hierarchical clustering can be viewed as sequence of partitional clusterings anda partitional clustering can be obtained by taking any member of that sequence; by cutting the hierarchical tree at a particular level.