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Algorithms
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Optimal Transport: Algorithms and Applications
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Optimal Transport: Algorithms and Applications

A special issue of Algorithms (ISSN 1999-4893). This special issue belongs to the section "Evolutionary Algorithms and Machine Learning".

Deadline for manuscript submissions: closed (31 October 2021) | Viewed by 7853

Special Issue Editor

Dr. Nicolas Bonneel

E-Mail Website
Guest Editor
CNRS, Lyon, France
Interests: optimal transport; image and video processing; geometry; rendering

Special Issue Information

Dear Colleagues,

Optimal transport is an increasingly popular tool with a wide range of applications, from machine learning to computer graphics, through econometrics, astrophysics, optics, image processing, fluid mechanics, genomics and many others.  At the same time, the growing amount of available data and successful algorithms has led machine learning to develop at an unprecedented rate. While optimal transport has been adopted by this community (as well), in many cases it suffers from prohibitive computational costs limiting its uses.

Research is needed to make this tool tractable for large scale datasets and efficient at smaller scale, and to express all of its potential via applications.

We invite you to submit high quality manuscripts to this special issue on "Optimal Transport: Algorithms and Applications". Topics of interest include (but are not limited to):

* Fast optimal transport algorithms (for transport plans, distances, barycenters etc.)

* Approximations of optimal transport, including regularizations, embeddings, or complete reformulations of the problem

* Interactions between machine learning and optimal transport

* Unexpected or fruitful applications of optimal transport

Dr. Nicolas Bonneel
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Algorithms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Optimal transport solvers
  • Optimal transport approximation algorithms
  • Optimal transport in machine learning
  • Applications of optimal transport

Published Papers (2 papers)

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Research

29 pages, 2397 KiB  
Article
Subspace Detours Meet Gromov–Wasserstein
by Clément Bonet, Titouan Vayer, Nicolas Courty, François Septier and Lucas Drumetz
Algorithms 2021, 14(12), 366; https://0-doi-org.brum.beds.ac.uk/10.3390/a14120366 - 17 Dec 2021
Cited by 2 | Viewed by 2533
Abstract
In the context of optimal transport (OT) methods, the subspace detour approach was recently proposed by Muzellec and Cuturi. It consists of first finding an optimal plan between the measures projected on a wisely chosen subspace and then completing it in a nearly [...] Read more.
In the context of optimal transport (OT) methods, the subspace detour approach was recently proposed by Muzellec and Cuturi. It consists of first finding an optimal plan between the measures projected on a wisely chosen subspace and then completing it in a nearly optimal transport plan on the whole space. The contribution of this paper is to extend this category of methods to the Gromov–Wasserstein problem, which is a particular type of OT distance involving the specific geometry of each distribution. After deriving the associated formalism and properties, we give an experimental illustration on a shape matching problem. We also discuss a specific cost for which we can show connections with the Knothe–Rosenblatt rearrangement. Full article
(This article belongs to the Special Issue Optimal Transport: Algorithms and Applications)
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16 pages, 645 KiB  
Article
Overrelaxed Sinkhorn–Knopp Algorithm for Regularized Optimal Transport
by Alexis Thibault, Lénaïc Chizat, Charles Dossal and Nicolas Papadakis
Algorithms 2021, 14(5), 143; https://0-doi-org.brum.beds.ac.uk/10.3390/a14050143 - 30 Apr 2021
Cited by 8 | Viewed by 4044
Abstract
This article describes a set of methods for quickly computing the solution to the regularized optimal transport problem. It generalizes and improves upon the widely used iterative Bregman projections algorithm (or Sinkhorn–Knopp algorithm). We first proposed to rely on regularized nonlinear acceleration schemes. [...] Read more.
This article describes a set of methods for quickly computing the solution to the regularized optimal transport problem. It generalizes and improves upon the widely used iterative Bregman projections algorithm (or Sinkhorn–Knopp algorithm). We first proposed to rely on regularized nonlinear acceleration schemes. In practice, such approaches lead to fast algorithms, but their global convergence is not ensured. Hence, we next proposed a new algorithm with convergence guarantees. The idea is to overrelax the Bregman projection operators, allowing for faster convergence. We proposed a simple method for establishing global convergence by ensuring the decrease of a Lyapunov function at each step. An adaptive choice of the overrelaxation parameter based on the Lyapunov function was constructed. We also suggested a heuristic to choose a suitable asymptotic overrelaxation parameter, based on a local convergence analysis. Our numerical experiments showed a gain in convergence speed by an order of magnitude in certain regimes. Full article
(This article belongs to the Special Issue Optimal Transport: Algorithms and Applications)
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