论文标题
内核K均值几乎最佳的聚类风险范围
Nearly Optimal Clustering Risk Bounds for Kernel K-Means
论文作者
论文摘要
在本文中，我们研究了内核$ k $ -MEANS的统计特性，并获得了几乎最佳的过剩聚类风险约束，从而在现有的聚类风险分析中显着提高了最新的界限。我们进一步分析了NyStrömKernel$ k $ -Means的计算近似值的统计效应，并证明它与仅考虑$ω（\ sqrt {nk}）的确切核心$ k $ -Means具有相同的统计准确性。据我们所知，以前从未提出过这种内核（或近似内核）$ k $ -MEANS的急剧多余的聚类风险范围。
In this paper, we study the statistical properties of kernel $k$-means and obtain a nearly optimal excess clustering risk bound, substantially improving the state-of-art bounds in the existing clustering risk analyses. We further analyze the statistical effect of computational approximations of the Nyström kernel $k$-means, and prove that it achieves the same statistical accuracy as the exact kernel $k$-means considering only $Ω(\sqrt{nk})$ Nyström landmark points. To the best of our knowledge, such sharp excess clustering risk bounds for kernel (or approximate kernel) $k$-means have never been proposed before.
