Locally Private k-Means in One Round
This work addresses privacy-preserving clustering for data analysis, providing a significant improvement in accuracy and efficiency for applications requiring local differential privacy.
The paper tackles the problem of k-means clustering in the one-round local differential privacy model, achieving an approximation ratio arbitrarily close to the best non-private algorithms, which improves upon prior constant-factor approximations and resolves an open question.
We provide an approximation algorithm for k-means clustering in the one-round (aka non-interactive) local model of differential privacy (DP). This algorithm achieves an approximation ratio arbitrarily close to the best non private approximation algorithm, improving upon previously known algorithms that only guarantee large (constant) approximation ratios. Furthermore, this is the first constant-factor approximation algorithm for k-means that requires only one round of communication in the local DP model, positively resolving an open question of Stemmer (SODA 2020). Our algorithmic framework is quite flexible; we demonstrate this by showing that it also yields a similar near-optimal approximation algorithm in the (one-round) shuffle DP model.