# Mini-Batch Kernel k-means

arXiv: https://arxiv.org/abs/2410.05902 · HTML: https://mlsanity.com/paper/2410.05902/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 31 references that are in the map.
- First posted on arXiv 8 Oct 2024.

## Builds on (most cited first, 6 of 6)

- [Turning Big data into tiny data: Constant-size coresets for k-means, PCA and projective clustering](https://mlsanity.com/paper/1807.04518/) (2018)
- [The Impact of Random Models on Clustering Similarity](https://mlsanity.com/paper/1701.06508/) (2017)
- [Convergence rate of stochastic k-means](https://mlsanity.com/paper/1611.05132/) (2016)
- [Coresets for Kernel Clustering](https://mlsanity.com/paper/2110.02898/) (2021)
- [Relative Error Embeddings for the Gaussian Kernel Distance](https://mlsanity.com/paper/1602.05350/) (2016)
- [Fast Approximation of Similarity Graphs with Kernel Density Estimation](https://mlsanity.com/paper/2310.13870/) (2023)

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

- [Coreset Spectral Clustering](https://mlsanity.com/paper/2503.07227/) (2025)

## Abstract (arXiv)

We present the first mini-batch kernel k-means algorithm, offering an order of magnitude improvement in running time compared to the full batch algorithm. A single iteration of our algorithm takes widetildeO(kb2) time, significantly faster than the O(n2) time required by the full batch kernel k-means, where n is the dataset size and b is the batch size. Extensive experiments demonstrate that our algorithm consistently achieves a 10-100x speedup with minimal loss in quality, addressing the slow runtime that has limited kernel k-means adoption in practice. We further complement these results with a theoretical analysis under an early stopping condition, proving that with a batch size of widetildeOmega(max γ4, γ2 · ε-2), the algorithm terminates in O(γ2/ε) iterations with high probability, where γ bounds the norm of points in feature space and ε is a termination threshold. Our analysis holds for any reasonable center initialization, and when using k-means++ initialization, the algorithm achieves an approximation ratio of O(log k) in expectation. For normalized kernels, such as Gaussian or Laplacian it holds that γ=1. Taking ε = O(1) and b=Theta(log n), the algorithm terminates in O(1) iterations, with each iteration running in widetildeO(k) time.