Tesselation and Clustering by Mixture Models and Their Parallel Implementations

Clustering and tessellations are basic tools in data mining. The k-means and EM algorithms are two of the most important algorithms in the Mixture Model-based clustering and tessellations. In this paper, we introduce a new clustering strategy which shares common features with both the EM and k-means algorithms. Our methods also lead to more general tessellations of a spatial region with respect to a continuous and possibly anisotropic density distribution. Moreover, we propose some probabilistic methods for the construction of these clusterings and tessellations corresponding to a continuous density distribution. Some numerical examples are presented to demonstrate the effectiveness of our new approach. In addition, we also discuss the parallel implementation and performance of our algorithms on some distributed memory systems.