Premium
Sample‐Based Optimal Transport and Barycenter Problems
Author(s) -
Kuang Max,
Tabak Esteban G.
Publication year - 2019
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21848
Subject(s) - mathematics , sample (material) , mathematical optimization , nonlinear system , decomposition , feature (linguistics) , characterization (materials science) , transportation theory , algorithm , ecology , linguistics , chemistry , physics , philosophy , materials science , chromatography , quantum mechanics , biology , nanotechnology
A methodology is developed for the numerical solution to the sample‐based optimal transport and Wasserstein barycenter problems. The procedure is based on a characterization of the barycenter and of the McCann interpolants that permits the decomposition of the global problem under consideration into various local problems where the distance among successive distributions is small. These local problems can be formulated in terms of feature functions and shown to have a unique minimizer that solves a nonlinear system of equations. Both the theoretical underpinnings of the methodology and its practical implementation are developed, and illustrated with synthetic and real data sets. © 2019 Wiley Periodicals, Inc.