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

TL;DR

This paper introduces global $k$-means$++$, a new clustering algorithm that achieves high-quality results similar to global $k$-means but with significantly reduced computational cost by leveraging $k$-means++ style center selection.

Contribution

The paper proposes the global $k$-means$++$ algorithm, combining the deterministic nature of global $k$-means with the probabilistic center selection of $k$-means++, reducing computational load while maintaining clustering quality.

Findings

Achieves comparable clustering quality to global $k$-means.

Reduces computational time significantly.

Performs well on various benchmark datasets.

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.