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

• URL: http://arxiv.org/abs/2211.12271v3
• Date: Fri, 14 Jul 2023 11:39:36 GMT
• Title: Global $k$-means$++$: an effective relaxation of the global $k$-means clustering algorithm
• Authors: Georgios Vardakas and Aristidis Likas
• Abstract summary: The $k$-means algorithm is a prevalent clustering method due to its simplicity, effectiveness, and speed. We propose the emphglobal $k$-meanstexttt++ clustering algorithm, which is an effective way of acquiring quality clustering solutions.
• Score: 0.20305676256390928
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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