Bounding box representation of co-location instances for Chebyshev and Manhattan metrics

Co-location Pattern Mining (CPM) is the task of discovering sets of spatial features (object types) whose instances are frequently located close to each other in space. Popular co-location discovery methods consist of iteratively: (1) generating co-location candidates, (2) determining instances of these candidates and calculating a measure of potential interestingness, and (3) determining the set of co-locations based on that measure. In this paper, we focus on the second step, as it is the most time-consuming element of CPM. We assume that the distance function is either the Chebyshev or the Manhattan metric. We provide an instance identification method that is characterized by a lower complexity than the state-of-the-art approach. In particular, (1) we introduce a new representation of co-location instances based on bounding boxes, (2) we formulate and prove several theorems regarding such a representation that can improve instances identification step, (3) we provide a novel algorithm that uses the above-mentioned theorems, and (4) we analyze its complexity. To verify our approach, we performed a series of experiments using two real-world datasets.