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Voronoi diagram and spatial clustering in the presence of obstacles

机译：有障碍物时的Voronoi图和空间聚类

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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, P_i and P_j, The Voronoi distance is defined that the minimum object Voronoi regions number between P_i and P_j 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.
机译：空间数据挖掘中的聚类是根据相似对象的距离，连通性或它们在空间中的相对密度对它们进行分组。聚类算法通常使用欧几里得距离。在现实世界中，存在许多物理障碍，例如河流，湖泊和公路，它们的存在可能会严重影响群集的结果。在本文中，我们研究了存在障碍物时的聚类问题，并在Voronoi图（蒂森多边形）中通过Voronoi距离提出了空间聚类。 Voronoi图具有横向空间邻接特征。在此基础上，我们可以方便地表达空间横向邻接关系，解决存在障碍物时空间聚类的问题。该方法包括三个步骤。首先，在存在障碍的情况下构建Voronoi图。其次，定义Voronoi距离。基于Voronoi图，我们提出了Voronoi距离。给定两个空间对象P_i和P_j，将Voronoi距离定义为：最小对象Voronoi区域在Voronoi图中位于P_i和P_j之间。第三，我们提出跟随障碍算法（FOA）。 FOA包括三个步骤：初始化步骤，查询步骤和修剪步骤。通过FOA，我们可以获得任意两个对象之间的Voronoi距离。通过Voronoi图和FOA，可以方便且更精确地完成存在障碍物的空间聚类。我们进行了各种性能研究，表明该方法既有效又有效。

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