  We propose to align distributional data from the perspective of Wasserstein
means. We raise the problem of regularizing Wasserstein means and propose
several terms tailored to tackle different problems. Our formulation is based
on the variational transportation to distribute a sparse discrete measure into
the target domain. The resulting sparse representation well captures the
desired property of the domain while reducing the mapping cost. We demonstrate
the scalability and robustness of our method with examples in domain
adaptation, point set registration, and skeleton layout.
