Topological Cluster: A Generalized View for Density-based Spatial Clustering

Clustering analysis has become an important tool in knowledge engineering and business intelligence. There are rapidly growing number of clustering algorithms, however, one of the most important clustering algorithms is the density based spatial clustering, and its various variations. These algorithms are either based on the density connected chains, or weighted density, or the gravity based connected sets. They seem similar in idea but there does not exist a unified presentation. The purpose of this paper is to give a topological view to the spatial clustering focusing on density based clustering with its variations. We propose the definition of cluster topology, define clusters as various kinds of topological connected sets. More in this paper, the topological cluster forming algorithms are presented. Then we reform some typical algorithms with the new topological view. Examples are given to show the theories.