Effective and Efficient Boundary-based Clustering for Three-dimensional Geoinformation Studies

Due to their inherent volumetric nature, underground and marine geoinformation studies and even astronomy demand clustering techniques capable of dealing with threedimensional data. However, most robust and exploratory spatial clustering approaches for GIS only consider two dimensions. We extend robust argument-free two-dimensional boundary-based clustering [8] to three dimensions. The progression to 3D demands manipulation of one argument from users and the encoding of proximity and density information in different proximity graphs. Fortunately, the input argument allows exploration of weaknesses in clusters, and detection of regions for potential merge or split. We also provide an effective heuristic to obtain good initial values for the input argument. This maximizes user friendliness and minimizes exploration time. Experimental results demonstrate that for two popular proximity graphs (Delaunay Tetrahedrization and undirected k-nearest neighbor graph) our approach is robust to the presence of noise and is able to detect high-quality volumetric clusters for complex situations such as non-convex clusters, clusters of different densities and clusters of different sizes. Our experiments also show that, undirected k-nearest neighbor graphs produce consistent high-quality clusters with little sensitivity to values of k. Moreover, this variant of the algorithm only requires subquadratic time. 1