Genetic K-means algorithm

In this paper, we propose a novel hybrid genetic algorithm (GA) that finds a globally optimal partition of a given data into a specified number of clusters. GA's used earlier in clustering employ either an expensive crossover operator to generate valid child chromosomes from parent chromosomes or a costly fitness function or both. To circumvent these expensive operations, we hybridize GA with a classical gradient descent algorithm used in clustering viz., K-means algorithm. Hence, the name genetic K-means algorithm (GKA). We define K-means operator, one-step of K-means algorithm, and use it in GKA as a search operator instead of crossover. We also define a biased mutation operator specific to clustering called distance-based-mutation. Using finite Markov chain theory, we prove that the GKA converges to the global optimum. It is observed in the simulations that GKA converges to the best known optimum corresponding to the given data in concurrence with the convergence result. It is also observed that GKA searches faster than some of the other evolutionary algorithms used for clustering.