We present a simple heuristic algorithm for efficiently optimizing the notoriously hard minimum sum-of-squares clustering problem, usually addressed by the classical k-means heuristic and its variants. The algorithm, called recombinator-k-means, is very similar to a genetic algorithmic scheme: it uses populations of configurations, that are optimized independently in parallel and then recombined in a next-iteration population batch by exploiting a variant of the k-means++ seeding algorithm. An additional reweighting mechanism ensures that the population eventually coalesces into a single solution. Extensive tests measuring optimization objective vs computational time on synthetic and real-word data show that it is the only choice, among state-of-the-art alternatives (simple restarts, random swap, genetic algorithm with pairwise-nearest-neighbor crossover), that consistently produces good results at all time scales, outperforming competitors on large and complicated datasets. The only parameter that requires tuning is the population size. The scheme is rather general (it could be applied even to k-medians or k-medoids, for example). Our implementation is publicly available at https://github.com/carlobaldassi/RecombinatorKMeans.jl.
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