A formalization of cluster analysis

摘要

This paper presents a formalization of the concept of cluster analysis. It begins with an intuitive description of clustering, and discusses the separation of the measurement problem from the clustering problem. It develops the nature of the elements to be clustered, the nature of the possible clusters, and the nature of the clustering results. Particularly significant is the introduction of the attribute of mass of an element. The paper defines a class of functions, called clustering functions, having a certain domain and range and satisfying a certain set of properties, called axioms. It discusses some properties which are inadequate to serve as axioms. Finally, it presents a function which is in the class of clustering functions.