Global k-means++: an effective relaxation of the global k-means clustering algorithm

The k-means algorithm is a prevalent clustering method due to its simplicity, effectiveness, and speed. However, its main disadvantage is its high sensitivity to the initial positions of the cluster centers. The global k-means is a deterministic algorithm proposed to tackle the random initialization problem of k-means but its well-known that requires high computational cost. It partitions the data to K clusters by solving all k-means sub-problems incrementally for all \({k=1,\ldots , K}\) $k=1,\dots ,K$ . For each k cluster problem, the method executes the k-means algorithm N times, where N is the number of datapoints. In this paper, we propose the global k-means++ clustering algorithm, which is an effective way of acquiring quality clustering solutions akin to those of global k-means with a reduced computational load. This is achieved by exploiting the center selection probability that is effectively used in the k-means++ algorithm. The proposed method has been tested and compared in various benchmark datasets yielding very satisfactory results in terms of clustering quality and execution speed.