Hierarchical Clustering

Abstract

Hierarchical clustering algorithms are mainly classified into agglomerative methods (bottom-up methods) and divisive methods (top-down methods), based on how the hierarchical dendrogram is formed. This chapter overviews the principles of hierarchical clustering in terms of hierarchy strategies, that is bottom-up or top-down, which correspond to agglomerative methods or divisive methods. There are many different definitions of the distance between clusters, which lead to different clustering algorithms/linkage techniques algorithms, namely single linkage, complete linkage, average linkage and Ward's linkage. There are two divisive algorithms, namely monothetic analysis (MONA) and divisive analysis (DIANA). DIANA splits up a cluster into two smaller ones, until finally all clusters contain only a single element. The chapter presents an example to illustrate the DIANA algorithm. MONA considers only binary variables, corresponding to the presence or absence of some attributes.