• Corpus ID: 25517366

# Scalable Kernel K-Means Clustering with Nystrom Approximation: Relative-Error Bounds

@article{Wang2019ScalableKK,
title={Scalable Kernel K-Means Clustering with Nystrom Approximation: Relative-Error Bounds},
author={Shusen Wang and Alex Gittens and Michael W. Mahoney},
journal={J. Mach. Learn. Res.},
year={2019},
volume={20},
pages={12:1-12:49}
}
• Published 9 June 2017
• Mathematics, Computer Science
• J. Mach. Learn. Res.
Kernel $k$-means clustering can correctly identify and extract a far more varied collection of cluster structures than the linear $k$-means clustering algorithm. However, kernel $k$-means clustering is computationally expensive when the non-linear feature map is high-dimensional and there are many input points. Kernel approximation, e.g., the Nystrom method, has been applied in previous works to approximately solve kernel learning problems when both of the above conditions are present. This…
63 Citations
Kernel k-Means, By All Means: Algorithms and Strong Consistency
• Computer Science, Mathematics
ArXiv
• 2020
This paper generalizes recent results leveraging a general family of means to combat sub-optimal local solutions to the kernel and multi-kernel settings and characterize the large sample behavior of the proposed method by establishing strong consistency guarantees.
On the optimality of kernels for high-dimensional clustering
• Mathematics, Computer Science
AISTATS
• 2020
This paper considers the problem of high-dimensional Gaussian clustering and shows that, with the exponential kernel function, the sufficient conditions for partial recovery of clusters using the NP-hard kernel k-means objective matches the known information-theoretic limit up to a factor of $\sqrt{2}$ for large $k$.
Fast Kernel k-means Clustering Using Incomplete Cholesky Factorization
• Computer Science, Mathematics
Appl. Math. Comput.
• 2021