Graph-Theoretic Methods of Cluster Analysis

Abstract

Two ways of defining clusters exist. Clusters can be defined constructively, by statement of a criterion and choice of an algorithm. The term “cluster” usually is left undefined. On the other hand, clusters can be defined as subsets of a sample S, satisfying certain mathematically convenient and evident conditions. In this axiomatic approach to classification theory, the term “cluster” is well-defined. Such pre-defined clusters are usually uncovered using measures of similarity, disparity, dissimilarity or distance, respectively. Rarely the raw data are used directly to find classes by outlining their shapes. In this chapter, we introduce cluster definitions, which are based on graph theory.