Regularized Wasserstein Means for Aligning Distributional Data

Wang G, Dong Q, Wu J, Su Y, Chen K, Su Q, Zhang X, Hao J, Yao T, Liu L, Zhang C, Caselli RJ, Reiman EM, Wang Y, ADNI Group 

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 and skeleton layout.

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Image of Regularized Wasserstein Means for Aligning Distributional Data
Image of Regularized Wasserstein Means for Aligning Distributional Data
Image of Regularized Wasserstein Means for Aligning Distributional Data
Image of Regularized Wasserstein Means for Aligning Distributional Data
Image of Regularized Wasserstein Means for Aligning Distributional Data
Image of Regularized Wasserstein Means for Aligning Distributional Data

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