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Noisy, Greedy and Not So Greedy k-means++
We show that this is not the case by presenting a family of instances on which greedy k-means++ yields only an $\Omega(\ell\cdot \log k)$-approximation in expectation where $\ell$ is the number of possible centers that are sampled in each iteration.
Analysis of Ward's Method
In this paper, we show that Ward's method computes a $2$-approximation with respect to the $k$-means objective function if the optimal $k$-clustering is well separated.
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