Clustering Methodology for Symbolic Data

7Divisive Hierarchical Clustering

A general overview of divisive hierarchical clustering was given in section 5.3. In the present chapter, we study this in detail as it pertains to symbolic data. Some basics relating to finding these clusters are first presented in section 7.1. Divisive clustering techniques are (broadly) either monothetic or polythetic methods. Monothetic methods involve one variable at a time considered successively across all variables. In contrast, polythetic methods consider all variables simultaneously. Each is considered in turn in sections 7.2 and 7.3, respectively. Typically, the underlying clustering criteria involve some form of distance or dissimilarity measure, and since for any set of data there can be many possible distance/dissimilarity measures, then the ensuing clusters are not necessarily unique across methods/measures. Recall, from Chapter 3 , that distances are dissimilarities for which the triangle property holds (see Definition 3.2). Therefore, the divisive techniques covered in this chapter use the generic “dissimilarity” measure unless it is a distance measure specifically under discussion. A question behind any clustering procedure relates to how many clusters is optimal. While there is no definitive answer to that question, some aspects are considered in section 7.4. Agglomerative hierarchical methods are considered in Chapter 8 .

7.1 Some Basics

7.1.1 Partitioning Criteria

In Chapters 3 and 4, we supposed our sample space consisted ...