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Classical spatial scan statistics are based on pre-defined shapes for scanning windows and specific distribution models and are used to detect latent cluster(s). However, the pre-defined windows (especially circularly shaped windows) may not be suitable for real situations, and the specific distribution models are inadequate for real clusters in which the exact distributions of the test statistics are only known in special cases. To generate more reasonable results, we propose a spatial scan statistic method with an irregularly shaped scanning window. A combinatorial particle swarm optimization method is used to optimize this window. A distribution-free concentration index is constructed to measure the difference between inside cluster and outside cluster. A compactness penalty function is employed to avoid generating clusters in a tree-structure. Simulation data sets are used to test the proposed method, and the results show the feasibility of our method.

Irregularly Shaped Cluster Detection Using a CPSO Distribution-Free Spatial Scan Statistic