This work addresses the problem of finding boundary points in multidimensional data sets. Boundary points are data points that are located at the margin of densely distributed data such as a cluster. We describe a novel approach called BORDER (a BOundaRy points DEtectoR) to detect such points. BORDER employs the state-of-the-art database technique - the Gorder kNN join and makes use of the special property of the reverse k nearest neighbor (RkNN). Experimental studies on data sets with varying characteristics indicate that BORDER is able to detect the boundary points effectively and efficiently.

The Reverse k-Nearest Neighbors (RkNN) queries are important in profile-based marketing, information retrieval, decision support and data mining systems. However, they are very expensive and existing algorithms are not scalable to queries in high dimensional spaces or of large values of k. This paper describes an efficient estimation-based RkNN search algorithm (ERkNN) which answers RkNN queries based on local kNN-distance estimation methods. The proposed approach utilizes estimation-based filtering strategy to lower the computation cost of RkNN queries. The results of extensive experiments on both synthetic and real life datasets demonstrate that ERkNN algorithm retrieves RkNN efficiently and is scalable with respect to data dimensionality, k, and data size.