Kernel K-means clustering of distributional data

• URL: http://arxiv.org/abs/2509.18037v1
• Date: Mon, 22 Sep 2025 17:11:29 GMT
• Title: Kernel K-means clustering of distributional data
• Authors: Amparo Baíllo, Jose R. Berrendero, Martín Sánchez-Signorini,
• Abstract summary: We consider the problem of clustering a sample of probability distributions from a random distribution on $mathbb Rp$.<n>Our proposed partitioning method makes use of a symmetric, positive-definite kernel $k$ and its associated reproducing kernel Hilbert space $mathcal H$.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $p>1$. 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.

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