Criteria on Proximity Graphs for Boundary Extraction and Spatial Clustering

Abstract

Proximity and density information modeling of 2D point-data by Delaunay Diagrams has delivered a powerful exploratory and argument-free clustering algorithm [6] for geographical data mining [13]. The algorithm obtains cluster boundaries using a Short-Long criterion and detects non-convex clusters, high and low density clusters, clusters inside clusters and many other robust results. Moreover, its computation is linear in the size of the graph used. This paper demonstrates that the criterion remains effective for exploratory analysis and spatial data mining where other proximity graphs are used. It also establishes a hierarchy of the modeling power of several proximity graphs and presents how the argument free characteristic of the original algorithm can be traded for argument tuning. This enables higher than 2 dimensions by using linear size proximity graphs like k-nearest neighbors.