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On the computation of Wasserstein barycenters
Journal Contribution - Journal Article
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 then-coupling problem. As a consequence, the coupling to the sum principle (characterizing solutions to then-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.
Journal: Journal of Multivariate Analysis
ISSN: 0047-259X
Volume: 176
Publication year:2020
CSS-citation score:1
Accessibility:Closed