# Kernel K-means clustering of distributional data

arXiv: https://arxiv.org/abs/2509.18037 · HTML: https://mlsanity.com/paper/2509.18037/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 44 references that are in the map.
- First posted on arXiv 22 Sep 2025.

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

- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Statistical Aspects of Wasserstein Distances](https://mlsanity.com/paper/1806.05500/) (2018)
- [Robust clustering tools based on optimal transportation](https://mlsanity.com/paper/1607.01179/) (2016)
- [Hybrid Wasserstein Distance and Fast Distribution Clustering](https://mlsanity.com/paper/1812.11026/) (2018)
- [Selection of the Number of Clusters in Functional Data Analysis](https://mlsanity.com/paper/1905.00977/) (2019)
- [Scalable Learning from Probability Measures with Mean Measure Quantization](https://mlsanity.com/paper/2502.04907/) (2025)

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

- [Nonparametric Kernel Clustering with Bandit Feedback](https://mlsanity.com/paper/2601.07535/) (2026)

## Abstract (arXiv)

We consider the problem of clustering a sample of probability distributions from a random distribution on mathbb Rp. Our proposed partitioning method makes use of a symmetric, positive-definite kernel k and its associated reproducing kernel Hilbert space (RKHS) mathcal H. By mapping each distribution to its corresponding kernel mean embedding in mathcal H, we obtain a sample in this RKHS where we carry out the K-means clustering procedure, which provides an unsupervised classification of the original sample. The procedure is simple and computationally feasible even for dimension p>1. The simulation studies provide insight into the choice of the kernel and its tuning parameter. The performance of the proposed clustering procedure is illustrated on a collection of Synthetic Aperture Radar (SAR) images.