Randomizing the Number of Centers in k-means++
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Computer Science > Data Structures and Algorithms
Title:Randomizing the Number of Centers in k-means++
Abstract:The $k$-means++ algorithm is a standard and widely used seeding method for $k$-means clustering, but for a fixed number $k$ of centers its worst-case expected approximation ratio is
$\Theta(\log k)$. We consider the same algorithm when an adversary first fixes the dataset and some $K$; the number of centers $k$ is then chosen uniformly from $\{K,\ldots,2K-1\}$.
We prove that $k$-means++ is an $O(1)$-approximation with constant probability in this budget-smoothed setup.
| Subjects: | Data Structures and Algorithms (cs.DS); Machine Learning (cs.LG); Machine Learning (stat.ML) |
| Cite as: | arXiv:2607.26202 [cs.DS] |
| (or arXiv:2607.26202v1 [cs.DS] for this version) | |
| https://doi.org/10.48550/arXiv.2607.26202
arXiv-issued DOI via DataCite (pending registration)
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