Online correlation clustering algorithm approximates all $\ell_p$-norms simultaneously

Researchers have developed a novel algorithm for online correlation clustering that can simultaneously approximate all $\ell_p$-norms. This algorithm, designed for the online-with-a-sample model, achieves competitive ratios of $O(\log^4 n)$ for all $\ell_p$-norms, $O(\log n)$ for the $\ell_\infty$-norm, and $O(1)$ for the $\ell_1$-norm. The work also introduces a new hardness result demonstrating a fundamental separation between $\ell_1$ and $\ell_\infty$ objectives in the standard random-order online model, showing that $\ell_\infty$ requires a competitive ratio of at least $\Omega(n^{1/3})$. AI

IMPACT Introduces a new theoretical framework for clustering that could impact data analysis and algorithm design in machine learning.

RANK_REASON The cluster contains an academic paper detailing a new algorithm and theoretical results in machine learning. [lever_c_demoted from research: ic=1 ai=1.0]

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• arXiv
• cs.LG
• $\ell_1$ norm
• $\ell_\infty$-norm
• $\ell_p$-norm
• Heather Newman
• Online Correlation Clustering

• paper
• other

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