Preconditioning of optimal transport

Max Kuang, Esteban Tabak

Research output: Contribution to journalArticle

Abstract

A preconditioning procedure is developed for the L2 and more general optimal transport problems. The procedure is based on a family of affine map pairs which transforms the original measures into two new measures that are closer to each other while preserving the optimality of solutions. It is proved that the preconditioning procedure minimizes the remaining transportation cost among all admissible affine maps. The procedure can be used on both continuous measures and finite sample sets from distributions. In numerical examples, the procedure is applied to multivariate normal distributions, to a two-dimensional shape transform problem, and to color-transfer problems.

Original languageEnglish (US)
Pages (from-to)A1793-A1810
JournalSIAM Journal on Scientific Computing
Volume39
Issue number4
DOIs
StatePublished - 2017

Fingerprint

Optimal Transport
Preconditioning
Normal distribution
Color
Transform
Multivariate Normal Distribution
Costs
Optimality
Minimise
Numerical Examples

Keywords

  • Matrix factorization
  • Optimal transport
  • Preconditioning

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this

Preconditioning of optimal transport. / Kuang, Max; Tabak, Esteban.

In: SIAM Journal on Scientific Computing, Vol. 39, No. 4, 2017, p. A1793-A1810.

Research output: Contribution to journalArticle

Kuang, Max ; Tabak, Esteban. / Preconditioning of optimal transport. In: SIAM Journal on Scientific Computing. 2017 ; Vol. 39, No. 4. pp. A1793-A1810.
@article{3d434fcf1860492db42b1af16323a9b8,
title = "Preconditioning of optimal transport",
abstract = "A preconditioning procedure is developed for the L2 and more general optimal transport problems. The procedure is based on a family of affine map pairs which transforms the original measures into two new measures that are closer to each other while preserving the optimality of solutions. It is proved that the preconditioning procedure minimizes the remaining transportation cost among all admissible affine maps. The procedure can be used on both continuous measures and finite sample sets from distributions. In numerical examples, the procedure is applied to multivariate normal distributions, to a two-dimensional shape transform problem, and to color-transfer problems.",
keywords = "Matrix factorization, Optimal transport, Preconditioning",
author = "Max Kuang and Esteban Tabak",
year = "2017",
doi = "10.1137/16M1074953",
language = "English (US)",
volume = "39",
pages = "A1793--A1810",
journal = "SIAM Journal of Scientific Computing",
issn = "1064-8275",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "4",

}

TY - JOUR

T1 - Preconditioning of optimal transport

AU - Kuang, Max

AU - Tabak, Esteban

PY - 2017

Y1 - 2017

N2 - A preconditioning procedure is developed for the L2 and more general optimal transport problems. The procedure is based on a family of affine map pairs which transforms the original measures into two new measures that are closer to each other while preserving the optimality of solutions. It is proved that the preconditioning procedure minimizes the remaining transportation cost among all admissible affine maps. The procedure can be used on both continuous measures and finite sample sets from distributions. In numerical examples, the procedure is applied to multivariate normal distributions, to a two-dimensional shape transform problem, and to color-transfer problems.

AB - A preconditioning procedure is developed for the L2 and more general optimal transport problems. The procedure is based on a family of affine map pairs which transforms the original measures into two new measures that are closer to each other while preserving the optimality of solutions. It is proved that the preconditioning procedure minimizes the remaining transportation cost among all admissible affine maps. The procedure can be used on both continuous measures and finite sample sets from distributions. In numerical examples, the procedure is applied to multivariate normal distributions, to a two-dimensional shape transform problem, and to color-transfer problems.

KW - Matrix factorization

KW - Optimal transport

KW - Preconditioning

UR - http://www.scopus.com/inward/record.url?scp=85028649917&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85028649917&partnerID=8YFLogxK

U2 - 10.1137/16M1074953

DO - 10.1137/16M1074953

M3 - Article

VL - 39

SP - A1793-A1810

JO - SIAM Journal of Scientific Computing

JF - SIAM Journal of Scientific Computing

SN - 1064-8275

IS - 4

ER -