A rejection-sampling based k-means++ seeding algorithm achieves O(log k)-competitive clusters with an additive error that decays exponentially in the number of sampling rounds, improving the prior linear decay.
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A New Rejection Sampling Approach to $k$-$\mathtt{means}$++ With Improved Trade-Offs
A rejection-sampling based k-means++ seeding algorithm achieves O(log k)-competitive clusters with an additive error that decays exponentially in the number of sampling rounds, improving the prior linear decay.