A Genetic XK-Means Algorithm with Empty Cluster Reassignment

K-Means is a well known and widely used classical clustering algorithm. It is easy to fall into local optimum and it is sensitive to the initial choice of cluster centers. XK-Means (eXploratory K-Means) has been introduced in the literature by adding an exploratory disturbance onto the vector of cluster centers, so as to jump out of the local optimum and reduce the sensitivity to the initial centers. However, empty clusters may appear during the iteration of XK-Means, causing damage to the efficiency of the algorithm. The aim of this paper is to introduce an empty-cluster-reassignment technique and use it to modify XK-Means, resulting in an EXK-Means clustering algorithm. Furthermore, we combine the EXK-Means with genetic mechanism to form a genetic XK-Means algorithm with empty-cluster-reassignment, referred to as GEXK-Means clustering algorithm. The convergence of GEXK-Means to the global optimum is theoretically proved. Numerical experiments on a few real world clustering problems are carried out, showing the advantage of EXK-Means over XK-Means, and the advantage of GEXK-Means over EXK-Means, XK-Means, K-Means and GXK-Means (genetic XK-Means).