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

Regularized Wasserstein Means for Aligning Distributional Data