A context-sensitive crossover operator for clustering applications

In this paper we propose a new context-sensitive crossover operator for genetic search based clustering applications. The proposed crossover operator compares relevant sub-regions in partitions represented by the two parents selected for mating, passing on to the child only high fitness sub-regions in the partition space. The use of the restricted growth function as the representation for the genotype makes it easier to do a meaningful cluster-wise comparison between two partitions. Clusters are compared using a statistical basis for spatial randomness on the assumption that natural groupings in data are compact and isolated and therefore spatially random within themselves. The proposed crossover operator has good exploitation properties and is heavily biased against an exploratory genetic search because it identifies and necessarily passes good schemas to the child. Preliminary results on two datasets of varying complexity tend to prove this point - when the proposed crossover operator is used with high probability, the search quickly homogenizes and moves as a whole towards high fitness regions of the partition space. We have also presented results of simulations where we have explicitly attempted to balance the exploitation and the exploration aspects of the search by using the crossover operator sparingly during the initial generations, thereby preserving diversity and letting the search branch off towards multiple local optima in the partition space.