Kernel K-means clustering of distributional data

2025/09/22 by Baíllo, Amparo, Berrendero, Jose R., Sánchez-Signorini, Martín
#Computation (stat.CO) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML)

paper · doi:10.48550/arxiv.2509.18037

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.

Citations

• Scalable Learning from Probability Measures with Mean Measure Quantization
• Statistical data analysis in the Wasserstein space
• Selection of the Number of Clusters in Functional Data Analysis
• Hybrid Wasserstein Distance and Fast Distribution Clustering
• Silhouettes: A graphical aid to the interpretation and validation of cluster analysis

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