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arXiv · 1802.00459

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

Wei Hu·Zhao Song·Lin F. Yang·Peilin Zhong
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Abstract

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

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Wei Hu, Zhao Song, Lin F. Yang, Peilin Zhong. 2018-02-01. Nearly Optimal Dynamic $k$-Means Clustering for High-Dimensional Data. https://arxiv.org/abs/1802.00459

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