Kernel $$K$$-Means Clustering of Distributional Data

Abstract

Abstract We consider the problem of clustering a sample of probability distributions from a random distribution on $$\mathbb R^d$$ R d . Our proposed partitioning method makes use of a symmetric, positive-definite kernel $$k$$ k and its associated reproducing kernel Hilbert space $$\mathscr {H}$$ H . By mapping each distribution to its corresponding kernel mean embedding in $$\mathscr {H}$$ H , we obtain a sample in this space where we carry out the $$K$$ K -means clustering procedure, which provides an unsupervised classification of the original sample. The procedure is simple and computationally feasible even for dimension $$d>1$$ d > 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 images and on meteorological data.