Minimum sum-of-squares clustering (MSSC) is a widely used clustering model, of which the popular K-means algorithm constitutes a local minimizer. It is well known that the solutions of K-means can be arbitrarily distant from the true MSSC global optimum, and dozens of alternative heuristics have been proposed for this problem. However, no other algorithm has been commonly adopted in the literature. This may be related to differences of computational effort, or to the assumption that a better solution of the MSSC has only a minor impact on classification or generalization capabilities. In this article, we dispute this belief. We introduce an efficient population-based metaheuristic that uses K-means as a local search in combination with problem-tailored crossover, mutation, and diversification operators. This algorithm can be interpreted as a multi-start K-means, in which the initial center positions are carefully sampled based on the search history. The approach is scalable and accurate, outperforming all recent state-of-the-art algorithms for MSSC in terms of solution quality, measured by the depth of local minima. This enhanced accuracy leads to classification results which are significantly closer to the ground truth than those of other algorithms, for overlapping Gaussian-mixture datasets with a large number of features and clusters. Therefore, improved global optimization methods appear to be essential to better exploit the MSSC model in high dimension.
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