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Related papers: Data representation with optimal transport

200 papers

It is shown that optimal network plans can be obtained, naturally, as a limit of easier problems of point allocations. These problems are obtained by minimizing the mass transportation on the set of atomic measures of prescribed number of…

Optimization and Control · Mathematics 2009-10-15 Gershon Wolansky

We propose a protocol optimization technique that is applicable to both weighted or unweighted graphs. Our aim is to explore by how much a small variation around the Shortest Path or Optimal Path protocols can enhance protocol performance.…

Physics and Society · Physics 2015-05-19 Jose J. Ramasco , Marta S. de la Lama , Eduardo Lopez , Stefan Boettcher

This paper provides a theoretical and numerical approach to show existence, uniqueness, and the numerical determination of metalenses refracting radiation with energy patterns. The theoretical part uses ideas from optimal transport and for…

Analysis of PDEs · Mathematics 2021-04-13 Cristian E. Gutiérrez , Qingbo Huang , Quentin Mérigot , Boris Thibert

In this paper we present a novel method for the numerical solution of linear transport equations, which is based on ridgelets. Such equations arise for instance in radiative transfer or in phase contrast imaging. Due to the fact that…

Numerical Analysis · Mathematics 2014-09-08 Philipp Grohs , Axel Obermeier

Many research has been conducted about quadratic programming and inverse optimization. In this paper we present the combination aspect of these subjects, applying on transportation problem. First, we obtain the inverse form of quadratic…

Optimization and Control · Mathematics 2014-09-25 Afrooz Jalilzadeh , Erfan Yazdandoost Hamedani

Non-additive measures, also known as fuzzy measures, capacities, and monotonic games, are increasingly used in different fields. Applications have been built within computer science and artificial intelligence related to e.g. decision…

Artificial Intelligence · Computer Science 2022-12-09 Vicenç Torra

In this work we propose a framework to address the issue of state dependent nonlinear equality-constrained state estimation using Bayesian filtering. This framework is constructed specifically for a linear approximation of Bayesian…

Optimization and Control · Mathematics 2020-03-16 Niladri Das , Raktim Bhattacharya

Learning from point sets is an essential component in many computer vision and machine learning applications. Native, unordered, and permutation invariant set structure space is challenging to model, particularly for point set…

Computer Vision and Pattern Recognition · Computer Science 2024-03-18 Mohammad Shifat E Rabbi , Naqib Sad Pathan , Shiying Li , Yan Zhuang , Abu Hasnat Mohammad Rubaiyat , Gustavo K Rohde

An efficient method for computing solutions to the Optimal Transportation (OT) problem with a wide class of cost functions is presented. The standard linear programming (LP) discretization of the continuous problem becomes intractible for…

Numerical Analysis · Mathematics 2015-09-15 Adam M. Oberman , Yuanlong Ruan

In this paper, we introduce a generalized dynamical unbalanced optimal transport framework by incorporating limited control input and mass dissipation, addressing limitations in conventional optimal transport for control applications. We…

Optimization and Control · Mathematics 2025-04-07 Dongjun Wu , Anders Rantzer

The Self-Optimal-Transport (SOT) feature transform is designed to upgrade the set of features of a data instance to facilitate downstream matching or grouping related tasks. The transformed set encodes a rich representation of high order…

Computer Vision and Pattern Recognition · Computer Science 2022-04-08 Daniel Shalam , Simon Korman

In this work, we solve a discrete optimal transport problem in a nonuniform environment. To solve the optimal transport problem, we build the cost matrix and then use classical solvers for discrete optimal transport. The challenge is to…

Optimization and Control · Mathematics 2026-03-17 Luca Dieci , Daniyar Omarov

Potential and mass barriers in graphene introduce electron scattering, modulating transmission probabilities. Complex multi-barrier setups allow electron transmission to be controlled with high precision, but have a huge design space of…

Mesoscale and Nanoscale Physics · Physics 2026-03-10 Leon Browne , Stephen R. Power

Optimal Transport, a theory for optimal allocation of resources, is widely used in various fields such as astrophysics, machine learning, and imaging science. However, many applications impose elementwise constraints on the transport plan…

Optimization and Control · Mathematics 2022-06-28 Zixuan Cang , Qing Nie , Yanxiang Zhao

We consider two variational models for transport networks, an urban planning and a branched transport model, in which the degree of network complexity and ramification is governed by a small parameter $\varepsilon>0$. Smaller $\varepsilon$…

Classical Analysis and ODEs · Mathematics 2017-11-16 Alessio Brancolini , Benedikt Wirth

We suggest a new way of defining optimal transport of positive-semidefinite matrix-valued measures. It is inspired by a recent rendering of the incompressible Euler equations and related conservative systems as concave maximization…

Optimization and Control · Mathematics 2019-07-16 Yann Brenier , Dmitry Vorotnikov

We present an optimal mass transport framework on the space of Gaussian mixture models, which are widely used in statistical inference. Our method leads to a natural way to compare, interpolate and average Gaussian mixture models.…

Probability · Mathematics 2018-02-01 Yongxin Chen , Tryphon T. Georgiou , Allen Tannenbaum

Optimal Transport (OT) problem aims to find a transport plan that bridges two distributions while minimizing a given cost function. OT theory has been widely utilized in generative modeling. In the beginning, OT distance has been used as a…

Machine Learning · Computer Science 2024-03-08 Jaemoo Choi , Jaewoong Choi , Myungjoo Kang

In this work, we propose a novel machine learning approach to compute the optimal transport map between two continuous distributions from their unpaired samples, based on the DeepParticle methods. The proposed method leads to a min-min…

Machine Learning · Statistics 2025-07-01 Yingyuan Li , Aokun Wang , Zhongjian Wang

Optimal Transport (OT) theory has seen an increasing amount of attention from the computer science community due to its potency and relevance in modeling and machine learning. It introduces means that serve as powerful ways to compare…

Machine Learning · Computer Science 2021-06-04 Luis Caicedo Torres , Luiz Manella Pereira , M. Hadi Amini