Chapter 13 - Clustering Algorithms II: Hierarchical Algorithms

Abstract

This chapter discusses the concept of hierarchical clustering algorithms. These algorithms produce a hierarchy of clustering and are usually found in the social sciences and biological taxonomy. They have also been used in many other fields, including modern biology, medicine, and archaeology. Applications of the hierarchical algorithms may also be found in computer science and engineering. Hierarchical clustering algorithms produce a hierarchy of nested clustering. These algorithms involve N steps, as many as the number of data vectors. A hierarchical algorithm can be viewed as a mapping of the data proximity matrix into a cophenetic matrix. The chapter explains in detail two main categories of hierarchical algorithms: the agglomerative and the divisive hierarchical algorithms. While explaining the general agglomerative scheme, the emphasis is on single link and complete link algorithms based on matrix theory. A special type of hierarchical algorithms that are most appropriate for handling large data sets is discussed. The need for such algorithms stems from a number of applications, such as Web mining and bioinformatics.