Finding aggregate proximity relationships and commonalities in spatial data mining

Abstract
Studies two spatial knowledge discovery problems involving proximity relationships between clusters and features. The first problem is: given a cluster of points, how can we efficiently find features (represented as polygons) that are closest to the majority of points in the cluster? We measure proximity in an aggregate sense due to the nonuniform distribution of points in a cluster (e.g. houses on a map), and the different shapes and sizes of features (e.g. natural or man-made geographic features). The second problem is: given n clusters of points, how can we extract the aggregate proximity commonalities (i.e. features) that apply to most, if not all, of the n clusters? Regarding the first problem, the main contribution of the paper is the development of Algorithm CRH (Circle, Rectangle and Hull), which uses geometric approximations (i.e. encompassing circles, isothetic rectangles and convex hulls) to filter and select features. The highly scalable and incremental Algorithm CRH can examine over 50,000 features and their spatial relationships with a given cluster in approximately one second of CPU time. Regarding the second problem, the key contribution is the development of Algorithm GenCom (Generalization for Commonality extraction) that makes use of concept generalization to effectively derive many meaningful commonalities that cannot be found otherwise.

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