MSPP: A Highly Efficient and Scalable Algorithm for Mining Similar Pairs of Points (2007.16111v1)

Abstract: The closest pair of points problem or closest pair problem (CPP) is an important problem in computational geometry where we have to find a pair of points from a set of points in metric space with the smallest distance between them. This problem arises in a number of applications, such as but not limited to clustering, graph partitioning, image processing, patterns identification, and intrusion detection. For example, in air-traffic control, we must monitor aircrafts that come too close together, since this may potentially indicate a possible collision. Numerous algorithms have been presented for solving the CPP. The algorithms that are employed in practice have a worst case quadratic run time complexity. In this article we present an elegant approximation algorithm for the CPP called MSPP: Mining Similar Pairs of Points. It is faster than currently best known algorithms while maintaining a very good accuracy. The proposed algorithm also detects a set of closely similar pairs of points in Euclidean and Pearson metric spaces and can be adapted in numerous real world applications, such as clustering, dimension reduction, constructing and analyzing gene/transcript co-expression network, among others.