Kernel K-means clustering of distributional data

M. Sánchez Signorini, A. Baíllo Moreno, J. R. Berrendero Díaz

We approach the problem of clustering a sample of probability distributions from a random distribution on R^p. By means of the maximum mean discrepancy (MMD) one can measure the distance between two probability distributions. As such, our proposed method considers a symmetric, positive-definite kernel k and its associated reproducing kernel Hilbert space H. After mapping the probability distributions to their kernel mean embedding in H, the K-means clustering algorithm is then applied in H, providing an unsupervised classification of the original sample. This procedure is straightforward and computationally feasible even for dimension p > 1. We present simulation studies to provide insight into the choice of the kernel and its tuning parameter. Furthermore, we illustrate the performance of our proposed clustering method on a collection of Synthetic Aperture Radar (SAR) images.

Keywords: Functional data, maximum mean discrepancy, nonparametric, unsupervised classification

GT AMyC II: Advances in Clustering and Regression Analysis
September 4, 2026  11:10 AM
Aula 28

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