Regularized Wasserstein Means for Aligning Distributional Data

TL;DR

This paper introduces a regularized Wasserstein means approach for aligning distributional data, enhancing scalability and robustness in applications like domain adaptation, point set registration, and skeleton layout.

Contribution

It develops a novel regularization framework for Wasserstein means using variational transportation, improving alignment quality and computational efficiency.

Findings

Effective in domain adaptation tasks

Robust in point set registration

Scalable to large datasets

Abstract

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.