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Unbalanced CO-Optimal Transport [article]

Quang Huy Tran, Hicham Janati, Nicolas Courty, Rémi Flamary, Ievgen Redko, Pinar Demetci, Ritambhara Singh
2022 arXiv   pre-print
CO-optimal transport (COOT) takes this comparison further by inferring an alignment between features as well.  ...  Optimal transport (OT) compares probability distributions by computing a meaningful alignment between their samples.  ...  In this work, we introduce an unbalanced extension of COOT called "Unbalanced CO-Optimal transport" (UCOOT).  ... 
arXiv:2205.14923v2 fatcat:svfxlgxvxnhyrlt7vss7i5k444

Semi-discrete unbalanced optimal transport and quantization [article]

David P. Bourne, Bernhard Schmitzer, Benedikt Wirth
2018 arXiv   pre-print
This class of unbalanced transport metrics allows for transport between measures of different total mass, unlike classical optimal transport where both measures must have the same total mass.  ...  We use this to develop an efficient method for solving the semi-discrete unbalanced transport problem numerically.  ...  What is unbalanced optimal transport? Classical optimal transport theory asks for the most efficient way to rearrange mass between two given probability distributions.  ... 
arXiv:1808.01962v1 fatcat:zeztm5x3mva2hfnmwyjn5xuuxm

Unbalanced Feature Transport for Exemplar-based Image Translation [article]

Fangneng Zhan, Yingchen Yu, Kaiwen Cui, Gongjie Zhang, Shijian Lu, Jianxiong Pan, Changgong Zhang, Feiying Ma, Xuansong Xie, Chunyan Miao
2021 arXiv   pre-print
We design a novel unbalanced optimal transport to address the transport between features with deviational distributions which exists widely between conditional inputs and exemplars.  ...  This paper presents a general image translation framework that incorporates optimal transport for feature alignment between conditional inputs and style exemplars in image translation.  ...  COS, OT and UOT mean to include cosine similarity, classical optimal transport and unbalanced optimal transport in feature alignment.  ... 
arXiv:2106.10482v1 fatcat:dj5rrmjy3jaqfdfe6oktodayrm

VMRF: View Matching Neural Radiance Fields [article]

Jiahui Zhang and Fangneng Zhan and Rongliang Wu and Yingchen Yu and Wenqing Zhang and Bai Song and Xiaoqin Zhang and Shijian Lu
2022 arXiv   pre-print
VMRF introduces a view matching scheme, which exploits unbalanced optimal transport to produce a feature transport plan for mapping a rendered image with randomly initialized camera pose to the corresponding  ...  With the feature transport plan as the guidance, a novel pose calibration technique is designed which rectifies the initially randomized camera poses by predicting relative pose transformations between  ...  Specifically, a view matching scheme with unbalanced optimal transport is designed to build an optimal transport plan to guide camera pose calibration.  ... 
arXiv:2207.02621v1 fatcat:wqtudg7mfbc6piil46tydxxcti

Unbalanced Optimal Transport: Dynamic and Kantorovich Formulation [article]

Lenaic Chizat and Gabriel Peyré and Bernhard Schmitzer and François-Xavier Vialard
2019 arXiv   pre-print
This article presents a new class of distances between arbitrary nonnegative Radon measures inspired by optimal transport.  ...  problem over pairs of couplings describing the transfer (transport, creation and destruction) of mass between two measures.  ...  Static formulations of unbalanced optimal transport. Purely static formulations of unbalanced transport are however a longstanding problem.  ... 
arXiv:1508.05216v3 fatcat:trlvynjqe5b3jigmto7creo7ky

Unsupervised integration of single-cell multi-omics datasets with disparities in cell-type representation [article]

Pinar Demetci, Rebecca Santorella, Bjorn Sandstede, Ritambhara Singh
2021 bioRxiv   pre-print
Here, we improve our previous work Single Cell alignment using Optimal Transport (SCOT) by using unbalanced optimal transport to handle disproportionate cell-type representation and differing sample sizes  ...  While recent unsupervised algorithms align single-cell multi-omic datasets, these methods have been primarily benchmarked on co-assay experiments rather than the more common single-cell experiments taken  ...  We thank Ievgen Redko, Ph.D. for useful discussions of optimal transport theory. Funding. Ritambhara Singh's contribution to the work is supported by NIH award 1R35HG011939-01.  ... 
doi:10.1101/2021.11.09.467903 fatcat:qopxeckxinh7nmx7dbb2xatwja

Scalable Unbalanced Optimal Transport using Generative Adversarial Networks [article]

Karren D. Yang, Caroline Uhler
2019 arXiv   pre-print
In this paper, we present a scalable method for unbalanced optimal transport (OT) based on the generative-adversarial framework.  ...  We formulate unbalanced OT as a problem of simultaneously learning a transport map and a scaling factor that push a source measure to a target measure in a cost-optimal manner.  ...  (b) Schematic of our formulation of unbalanced optimal transport.  ... 
arXiv:1810.11447v2 fatcat:gdhx34qzzjho5apg2xuozxv4jq

Dual Regularized Optimal Transport [article]

Rishi Sonthalia, Anna C. Gilbert
2020 arXiv   pre-print
In this paper, we present a new formulation of unbalanced optimal transport called Dual Regularized Optimal Transport (DROT).  ...  We argue that regularizing the dual formulation of optimal transport results in a version of unbalanced optimal transport that leads to sparse solutions and that gives us control over mass creation and  ...  Specifically, 1. the dual of DROT is a form of unbalanced optimal transport whose solution leads to sparse solutions to the optimal transport problem; 2.  ... 
arXiv:2012.03126v1 fatcat:x7dhioc5bzenjlpgmis4vqnt54

Optimal Transport for Diffeomorphic Registration [article]

Jean Feydy, François-Xavier Vialard
2017 arXiv   pre-print
This paper introduces the use of unbalanced optimal transport methods as a similarity measure for diffeomorphic matching of imaging data.  ...  We build on recent theoretical and numerical advances in optimal transport to propose fast and global similarity measures that can be used on surfaces or volumetric imaging data.  ...  Unbalanced optimal transport.  ... 
arXiv:1706.05218v1 fatcat:xghel4ra55hangqvh4o3lmruui

Optimal Transport for Diffeomorphic Registration [chapter]

Jean Feydy, Benjamin Charlier, François-Xavier Vialard, Gabriel Peyré
2017 Lecture Notes in Computer Science  
This paper introduces the use of unbalanced optimal transport methods as a similarity measure for diffeomorphic matching of imaging data.  ...  We build on recent theoretical and numerical advances in optimal transport to propose fast and global similarity measures that can be used on surfaces or volumetric imaging data.  ...  Unbalanced optimal transport.  ... 
doi:10.1007/978-3-319-66182-7_34 fatcat:psbnorpqbrh4bcuoh4vy25y3ga

Which Metric on the Space of Collider Events? [article]

Tianji Cai, Junyi Cheng, Katy Craig, Nathaniel Craig
2021 arXiv   pre-print
Motivated by the success of the Energy Mover's Distance in characterizing collider events, we explore the larger space of unbalanced optimal transport distances, of which the Energy Mover's Distance is  ...  Geometric and computational considerations favor an unbalanced optimal transport distance known as the Hellinger-Kantorovich distance, which possesses a Riemannian structure that lends itself to efficient  ...  JET CLASSIFICATION WITH UNBALANCED OPTIMAL TRANSPORT We now demonstrate the practical relevance of linearized, unbalanced optimal transport to collider physics by applying the pluOT framework to the task  ... 
arXiv:2111.03670v1 fatcat:gf5ia5m2wfddtbyd2deuirrcme

Scaling Algorithms for Unbalanced Transport Problems [article]

Lenaic Chizat, Gabriel Peyré, Bernhard Schmitzer, François-Xavier Vialard
2017 arXiv   pre-print
A generic class of such "unbalanced" optimal transport problems has been recently proposed by several authors.  ...  This article introduces a new class of fast algorithms to approximate variational problems involving unbalanced optimal transport.  ...  Definition 2.11 (Unbalanced Optimal Transport [47, Problem 3.1]).  ... 
arXiv:1607.05816v2 fatcat:lbqboh44dve6hp4xc4mgriw354

Application Of Transportation Linear Programming Algorithms To Cost Reduction In Nigeria Soft Drinks Industry

A. O. Salami
2014 Zenodo  
The transportation problems are primarily concerned with the optimal way in which products produced at different plants (supply origins) are transported to a number of warehouses or customers (demand destinations  ...  The result shows that the three methods produced the same total transportation costs amounting to N1, 358, 019, implying that any of the method can be adopted by the company in transporting its final products  ...  Unbalanced Transportation Problem The transportation is unbalanced when the total quantity demanded by the depots is not equal to the total supply or capacity of the plants.  ... 
doi:10.5281/zenodo.1090637 fatcat:rf7knynngrezjkoriva3sjpwby

Optimal Transport for Manifold-Valued Images [chapter]

Jan Henrik Fitschen, Friederike Laus, Bernhard Schmitzer
2017 Lecture Notes in Computer Science  
Applying recently introduced 'unbalanced' optimal transport models leads to more natural results.  ...  We introduce optimal transport-type distances for manifoldvalued images.  ...  This is expected, as optimal transport does not explicitly enforce spatial regularity of the optimal matching.  ... 
doi:10.1007/978-3-319-58771-4_37 fatcat:5zckpg55fndrhkpi5er3hwykgu

Optimal Tensor Transport

Tanguy Kerdoncuff, Rémi Emonet, Michael Perrot, Marc Sebban
2022 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
To expand the range of possible applications, Co-Optimal Transport (Co-OT) jointly estimates two distinct transport plans, one for the rows (points) and one for the columns (features), to match two data  ...  In this paper, we propose a unified framework, called Optimal Tensor Transport (OTT), which takes the form of a generic formulation that encompasses OT, GW and Co-OT and can handle tensors of any order  ...  Co-Optimal Transport (Redko et al. 2020) . Co-Optimal Transport also aims at transporting points from two datasets X and Y .  ... 
doi:10.1609/aaai.v36i7.20672 fatcat:qmwicf6gxnacppchndp7y2al3y
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