Illustrate the hierarchical clustering with an example.

 The hierarchical clustering method produces a set of nested clusters organized as a hierarchical tree by performing Hierarchical decomposition (merge or split) of data point's based on a similarity or distance matrix Depending on whether the hierarchical decomposition is formed in a bottom-up (merging) or top-down (splitting) fashion a hierarchical clustering method can be classified into two main categories. While partitioning methods meet the basic clustering requirement of organizing a set of objects into a number of exclusive groups, in some situations we may want to partition our data into groups at different levels such as in a hierarchy. A hierarchical clustering method works by grouping data objects into a hierarchy or "tree" of clusters. They are: Agglomerative hierarchical clustering, Divisive hierarchical clustering

Examples of hierarchical clustering is given below:-

1) While partitioning methods meet the basic clustering requirement of organizing a set of objects into a number of exclusive groups, in some situations we may want to partition our data into groups at different levels such as in a hierarchy. A hierarchical clustering method works by grouping data objects into a hierarchy or "tree" of clusters. 

2) Representing data objects in the form of a hierarchy is useful for data summarization and visualization. For example, as the manager of human resources at AllElectronics,you may organize your employees into major groups such as executives, managers, and staff. You can further partition these groups into smaller subgroups. For instance, the general group of staff can be further divided into subgroups of senior officers, officers, and trainees. All these groups form a hierarchy. We can easily summarize or characterize the data that are organized into a hierarchy, which can be used to find, say, the average salary of managers and of officers.

3) Consider handwritten character recognition as another example. A set of handwriting samples may be first partitioned into general groups where each group corresponds to a unique character. Some groups can be further partitioned into subgroups since a character may be written in multiple substantially different ways. If necessary, the hierarchical partitioning can be continued recursively until the desired granularity is reached.

4) In the previous examples, although we partitioned the data hierarchically, we did not assume that the data have a hierarchical structure (e.g., managers are at the same level in our AllElectronics hierarchy as staff). Our use of a hierarchy here is just to summarize and represent the underlying data in a compressed way. Such a hierarchy is particularly useful for data visualization.

5) Alternatively, in some applications, we may believe that the data bear an underlying hierarchical structure that we want to discover. For example, hierarchical clustering may uncover a hierarchy for AllElectronics employees structured on, say, salary. In the study of evolution, hierarchical clustering may group animals according to their biological features to uncover evolutionary paths, which are a hierarchy of species. As another example, grouping configurations of a strategic game (e.g., chess or checkers) in a hierarchical way may help to develop game strategies that can be used to train players.