Boundary Points Detection Using Adjacent Grid Block Selection (AGBS) kNN-Join Method

Interpretability, usability, and boundary points detection of the clustering results are of fundamental importance. The cluster boundary detection is important for many real world applications, such as geo-spatial data analysis and point-based computer graphics. In this paper, we have proposed an efficient solution for finding boundary points in multi-dimensional datasets that uses the BORDER [1] method as a foundation which is based on Gorder knearest neighbors (kNN) join [10]. We have proposed an Adjacent Grid Block Selection (AGBS) method to compute the kNN-join of two datasets. Further, the AGBS method has been used for the boundary points detection method named as AGBS-BORDER. It executes AGBS join for each element in the dataset to get the paired (qi, pi) kNN values. The kNN-graphs are generated at the same time while computing the kNN-join of the underlying datasets. The nodes maintain a list of kNN which indicate the outgoing edges of the graph; however the incoming edges denote the Reverse kNN (RkNN) for the corresponding nodes. Finally, threshold filter is applied the node whose number of RkNN is less than the threshold values are marked as the border nodes. We have implemented both the BORDER [1] and AGBS-BORDER methods and tested the same using randomly generated geographical points. The AGBS based boundary computation over performs the existing BORDER method.