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The $k$-means algorithm is a prevalent clustering method due to itssimplicity, effectiveness, and speed. However, its main disadvantage is itshigh sensitivity to the initial positions of the cluster centers. The global$k$-means is a deterministic algorithm proposed to tackle the randominitialization problem of k-means but its well-known that requires highcomputational cost. It partitions the data to $K$ clusters by solving all$k$-means sub-problems incrementally for all $k=1,\ldots, K$. 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 \emph{global$k$-means\texttt{++}} clustering algorithm, which is an effective way ofacquiring quality clustering solutions akin to those of global $k$-means with areduced computational load. This is achieved by exploiting the center selectionprobability that is effectively used in the $k$-means\texttt{++} algorithm. Theproposed method has been tested and compared in various benchmark datasetsyielding very satisfactory results in terms of clustering quality and executionspeed.

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