Voronoi diagram and spatial clustering in the presence of obstacles

Abstract

Clustering in spatial data mining is to group similar objects based on their distance, connectivity, or their relative density in space. Clustering algorithms typically use the Euclidean distance. In the real world, there exist many physical obstacles such as rivers, lakes and highways, and their presence may affect the result of clustering substantially. In this paper, we study the problem of clustering in the presence of obstacles and propose spatial clustering by Voronoi distance in Voronoi diagram (Thiessen polygon). Voronoi diagram has lateral spatial adjacency character. Based on it, we can express the spatial lateral adjacency relation conveniently and solve the problem derived from spatial clustering in the presence of obstacles. The method has three steps. First, building the Voronoi diagram in the presence of obstacles. Second, defining the Voronoi distance. Based on Voronoi diagram, we propose the Voronoi distance. Giving two spatial objects, <i>P_i</i> and <i>P_j</i>, The Voronoi distance is defined that the minimum object Voronoi regions number between <i>P_i</i> and <i>P_j</i> in the Voronoi diagram. Third, we propose Following-Obstacle-Algorithm (FOA). FOA includes three steps: the initializing step, the querying step and the pruning step. By FOA, we can get the Voronoi distance between any two objects. By Voronoi diagram and the FOA, the spatial clustering in the presence of obstacles can be accomplished conveniently, and more precisely. We conduct various performance studies to show that the method is both efficient and effective.