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We consider the $k$-means clustering problem in the dynamic streamingsetting, where points from a discrete Euclidean space $\{1, 2, \ldots,\Delta\}^d$ can be dynamically inserted to or deleted from the dataset. Forthis problem, we provide a one-pass coreset construction algorithm using space$\tilde{O}(k\cdot \mathrm{poly}(d, \log\Delta))$, where $k$ is the targetnumber of centers. To our knowledge, this is the first dynamic geometric datastream algorithm for $k$-means using space polynomial in dimension and nearlyoptimal (linear) in $k$.

Nearly Optimal Dynamic $k$-Means Clustering for High-Dimensional Data