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In this paper, the decades-old clustering method k-means is revisited. Theoriginal distortion minimization model of k-means is addressed by a purestochastic minimization procedure. In each step of the iteration, one sample istentatively reallocated from one cluster to another. It is moved to anothercluster as long as the reallocation allows the sample to be closer to the newcentroid. This optimization procedure converges faster to a better localminimum over k-means and many of its variants. This fundamental modificationover the k-means loop leads to the redefinition of a family of k-meansvariants. Moreover, a new target function that minimizes the summation ofpairwise distances within clusters is presented. We show that it could besolved under the same stochastic optimization procedure. This minimizationprocedure built upon two minimization models outperforms k-means and itsvariants considerably with different settings and on different datasets.

k-sums: another side of k-means