On the computation of Wasserstein barycenters

18 Pages Posted: 28 Nov 2018 Last revised: 1 Dec 2018

See all articles by Giovanni Puccetti

Giovanni Puccetti

University of Milan - Department of Economics, Management and Quantitative Methods (DEMM)

Ludger Rüschendorf

University of Freiburg

Steven Vanduffel

Vrije Universiteit Brussel (VUB)

Date Written: November 29, 2018

Abstract

In recent years, the Wasserstein barycenter has become 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. We give a new criterion for the explicit construction of barycenters generalizing the Gaussian case. Based on the n-coupling problem and an iterative version of the swapping algorithm, we introduce a new and simple algorithm to compute Wasserstein barycenters. We show in some examples that our approach is able to provide an accurate and fast visualization of barycenters even for a large number of marginals relevant for applications. The algorithm also provides an approximate solution for more complex optimization problems like the k-barycenter problem.

Keywords: Wasserstein barycenter, swapping algorithm, optimal transportations, k-means clustering, image processing

Suggested Citation

Puccetti, Giovanni and Rüschendorf, Ludger and Vanduffel, Steven, On the computation of Wasserstein barycenters (November 29, 2018). Available at SSRN: https://ssrn.com/abstract=3276147 or http://dx.doi.org/10.2139/ssrn.3276147

Giovanni Puccetti (Contact Author)

University of Milan - Department of Economics, Management and Quantitative Methods (DEMM) ( email )

Via Conservatorio, 7
Milan, 20122
Italy

Ludger Rüschendorf

University of Freiburg ( email )

Fahnenbergplatz
Freiburg, D-79085
Germany

Steven Vanduffel

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
Brussels, Brabant 1050
Belgium

HOME PAGE: http://www.stevenvanduffel.com

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