Many heuristics were developed recently to find arbitrarily shaped clusters (see review [1]). The most popular statistic is the spatial scan [2]. Nevertheless, even if all cluster solutions could be known, the problem of selecting the best cluster is ill posed. This happens because other measures, such as geometric regularity [3-5] or topology [6] must be taken intoconsideration. Most cluster finding methods does not address this last problem. A genetic multi-objective algorithm was developed elsewhere to identify irregularlyshaped clusters [5]. That method conducts a search aiming to maximize two objectives, namely the scan statistic and the regularity of shape (using the compactness concept).The solution presented is a Pareto-set, consisting of all the clusters found which are not simultaneously worse in both objectives. The significance evaluation is conducted in parallel for all the clusters in the Pareto-set through a Monte Carlo simulation, determining the best cluster solution.
Objective
Irregularly shaped clusters occur naturally in disease surveillance, but they are not well defined. The number of possible clusters increases exponentially with the number of regions in a map. This concurs to reduce the power of detection, motivating the utilization of some kind of penalty function to avoid excessive freedom of shape. We introduce a weak link based correction which penalizes inconsistent clusters, without forbidding the presence of the geographically interesting irregularly shaped ones.