Randomizing the Number of Centers in k-means++

• URL: http://arxiv.org/abs/2607.26202v1
• Date: Tue, 28 Jul 2026 19:06:53 GMT
• Title: Randomizing the Number of Centers in k-means++
• Abstract summary: The $k$-means++ algorithm is a standard and widely used seeding method for $k$-means clustering.<n>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 $K,ldots,2K-1$.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $Θ(\log k)$. 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.

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