# Nearly Optimal Clustering Risk Bounds for Kernel K-Means

arXiv: https://arxiv.org/abs/2003.03888 · HTML: https://mlsanity.com/paper/2003.03888/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Mar 2020.

## Built on by (most cited first, 1 of 1)

- [Smoothed Multi-View Subspace Clustering](https://mlsanity.com/paper/2106.09875/) (2021)

## Abstract (arXiv)

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 Nystr"om kernel k-means, and prove that it achieves the same statistical accuracy as the exact kernel k-means considering only Omega(√nk) Nystr"om 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.