Differentially Private k-Means with Constant Multiplicative Error
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We design new differentially private algorithms for the Euclidean k-means problem, both in the centralized model and in the local model of differential privacy. In both models, our algorithms achieve significantly improved error rates over the previous state-of-the-art. In addition, in the local model, our algorithm significantly reduces the number of needed interactions. Although the problem has been widely studied in the context of differential privacy, all of the existing constructions achieve only super constant approximation factors. We present, for the first time, efficient private algorithms for the problem with constant multiplicative error.
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