On the computation of Wasserstein barycenters

Giovanni Puccetti, Ludger Rüschendorf and Steven Vanduffel ()

Journal of Multivariate Analysis, 2020, vol. 176, issue C

Abstract: The Wasserstein barycenter is an important notion in the analysis of high dimensional data with a broad range of applications in applied probability, economics, statistics, and in particular to clustering and image processing. In this paper, we state a general version of the equivalence of the Wasserstein barycenter problem to the n-coupling problem. As a consequence, the coupling to the sum principle (characterizing solutions to the n-coupling problem) provides a novel criterion for the explicit characterization of barycenters. Based on this criterion, we provide as a main contribution the simple to implement iterative swapping algorithm (ISA) for computing barycenters. The ISA is a completely non-parametric algorithm which provides a sharp image of the support of the barycenter and has a quadratic time complexity which is comparable to other well established algorithms designed to compute barycenters. The algorithm can also be applied to more complex optimization problems like the k-barycenter problem.

Keywords: Image processing; k-means clustering; Optimal transportation; Swapping algorithm; Wasserstein barycenter (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.jmva.2019.104581

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