  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 $k=1,\ldots, K$. 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 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\texttt{++} 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.
