{"ID":2867850,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.18037","arxiv_id":"2509.18037","title":"Kernel K-means clustering of distributional data","abstract":"We consider the problem of clustering a sample of probability distributions from a random distribution on $\\mathbb R^p$. 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 $p\u003e1$. 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.","short_abstract":"We consider the problem of clustering a sample of probability distributions from a random distribution on $\\mathbb R^p$. 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 co...","url_abs":"https://arxiv.org/abs/2509.18037","url_pdf":"https://arxiv.org/pdf/2509.18037v1","authors":"[\"Amparo Baíllo\",\"Jose R. Berrendero\",\"Martín Sánchez-Signorini\"]","published":"2025-09-22T17:11:29Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\",\"stat.CO\"]","methods":"[]","has_code":false}