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We analyze online and mini-batch k-means variants. Both scale up the widely used Lloyd 's algorithm via stochastic approximation, and have become popular for large-scale clustering and unsupervised feature learning. We show, for the first time, that they have global convergence towards local optima at O(1/t) rate under general conditions. In addition, we show if the dataset is clusterable, with suitable initialization, mini-batch k-means converges to an optimal k-means solution with O(1/t)arXiv:1610.04900v2 fatcat:5zpfr3qxbjg4hebnbmgzud3y4e