Compactness, Connectivity or Cohesion? A New Penalty Function for Detecting Irregularly Shaped Cluster

Penalty functions are important for irregularly shaped spatial scan statistics to avoid overestimating of scanning results. Therefore, literature has proposed lots of penalty functions. Among these functions, non-compactness penalty function, non-connectivity penalty function, and internal cohesion penalty function are three mainstreams. In this paper, we propose a new penalty function to get more promising clusters. Unlike those three penalty functions, our function considers the difference between events' actual distribution and ideal distribution, does not avoid any other latent interesting irregularly shaped clusters and is more stable. Besides, a spatial scan statistic for irregularly shaped Combinatorial Particle Swarm Optimization (CPSO) combined with the new penalty function is introduced. Census data are used to assess our new penalty function, and the result shows the applicability of the CPSO spatial scan statistic and better performance of our new penalty function than the three other penalty functions.