English(EN) Low-degree polynomials lower bounds for clustering in small dimension

新下界挑战高维聚类算法

作者 PulseAugur 编辑部 · [1 个来源] · 2026-10-28 04:00

研究人员在高维设置下为聚类算法建立了新的理论下界。该研究侧重于簇数量远超数据维度的场景。通过构建基于双 BCH 码的伯努利分布混合，研究团队证明，即使簇中心之间存在对数级分离，聚类在计算上仍然具有挑战性。这种难度延伸到各向同性高斯混合模型，表明某些聚类方法存在根本性限制。 AI

影响确立了聚类算法的理论极限，可能指导无监督学习的未来研究。

排序理由详细介绍理论发现的学术论文。[lever_c_demoted from research: ic=1 ai=1.0]

AI 生成摘要 · Google Gemini · 来自 1 个来源。我们如何撰写摘要 →

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arXiv stat.ML TIER_1 English(EN) · Alexandra Carpentier (MISTEA), Nicolas Verzelen (MISTEA) · 2026-10-28 04:00

低度多项式在低维聚类中的下界

arXiv:2610.37272v1 Announce Type: new Abstract: We study the computational limits of clustering $n$ observations drawn from a mixture of $K$ isotropic distributions in $\mathbb R^d$, in the regime where the number $K$ of groups is much larger than the dimension $d$. In this regim…