Kernel K-means clustering of distributional data

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.