  The Wasserstein distance is a powerful metric based on the theory of optimal
transport. It gives a natural measure of the distance between two distributions
with a wide range of applications. In contrast to a number of the common
divergences on distributions such as Kullback-Leibler or Jensen-Shannon, it is
(weakly) continuous, and thus ideal for analyzing corrupted data. To date,
however, no kernel methods for dealing with nonlinear data have been proposed
via the Wasserstein distance. In this work, we develop a novel method to
compute the L2-Wasserstein distance in a kernel space implemented using the
kernel trick. The latter is a general method in machine learning employed to
handle data in a nonlinear manner. We evaluate the proposed approach in
identifying computerized tomography (CT) slices with dental artifacts in head
and neck cancer, performing unsupervised hierarchical clustering on the
resulting Wasserstein distance matrix that is computed on imaging texture
features extracted from each CT slice. Our experiments show that the kernel
approach outperforms classical non-kernel approaches in identifying CT slices
with artifacts.
