Data structures for minimization of total within-group distance for spatio-temporal clustering

Abstract

Statistical principles suggest minimization of the total withingroup distance (TWGD) as a robust criterion for clustering point data associated with a Geographical Information System [17]. This NP-hard problem must essentially be solved using heuristic methods, although admitting a linear programming formulation. Heuristics proposed so far require quadratic time, which is prohibitively expensive for data mining applications. This paper introduces data structures for the management of large bi-dimensional point data sets and for fast clustering via interchange heuristics. These structures avoid the need for quadratic time through approximations to proximity information. Our scheme is illustrated with two-dimensional quadtrees, but can be extended to use other structures suited to three dimensional data or spatial data with timestamps. As a result, we obtain a fast and robust clustering method.