HG-means: A scalable hybrid genetic algorithm for minimum sum-of-squares clustering
This work addresses the need for more accurate global optimization in clustering for high-dimensional data, though it is incremental as it builds on existing genetic and K-means approaches.
The paper tackles the problem of finding global optima for minimum sum-of-squares clustering (MSSC), where K-means often fails, by introducing a scalable hybrid genetic algorithm that combines K-means with tailored operators. The result is a method that outperforms recent state-of-the-art algorithms in solution quality, leading to clusters significantly closer to ground truth in high-dimensional datasets.
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 predominantly adopted in the literature. This may be related to differences of computational effort, or to the assumption that a near-optimal solution of the MSSC has only a marginal impact on clustering validity. 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 clusters which are significantly closer to the ground truth than those of other algorithms, for overlapping Gaussian-mixture datasets with a large number of features. Therefore, improved global optimization methods appear to be essential to better exploit the MSSC model in high dimension.