Computing Wasserstein Barycenter via operator splitting: the method of averaged marginals Article Swipe

View

Daniel Mimouni , Paul Malisani , Ji Zhu , Welington de Oliveira ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2309.05315

The Wasserstein barycenter (WB) is an important tool for summarizing sets of probability measures. It finds applications in applied probability, clustering, image processing, etc. When the measures' supports are finite, computing a (balanced) WB can be done by solving a linear optimization problem whose dimensions generally exceed standard solvers' capabilities. In the more general setting where measures have different total masses, we propose a convex nonsmooth optimization formulation for the so-called unbalanced WB problem. Due to their colossal dimensions, we introduce a decomposition scheme based on the Douglas-Rachford splitting method that can be applied to both balanced and unbalanced WB problem variants.Our algorithm, which has the interesting interpretation of being built upon averaging marginals, operates a series of simple (and exact) projections that can be parallelized and even randomized, making it suitable for large-scale datasets. Numerical comparisons against state-of-the-art methods on several data sets from the literature illustrate the method's performance.

Related Topics

Concepts

Operator (biology) Operator splitting Applied mathematics Mathematics Computer science Chemistry Transcription factor Repressor Gene Biochemistry

Metadata

Type: preprint
Language: en
Landing Page: https://doi.org/10.48550/arxiv.2309.05315
OA Status: green
References: 29
Related Works: 10
OpenAlex ID: https://openalex.org/W4386651498

All OpenAlex metadata

Raw OpenAlex JSON

OpenAlex ID: https://openalex.org/W4386651498

Canonical identifier for this work in OpenAlex
DOI: https://doi.org/10.48550/arxiv.2309.05315

Digital Object Identifier
Title: Computing Wasserstein Barycenter via operator splitting: the method of averaged marginals

Work title
Type: preprint

OpenAlex work type
Language: en

Primary language
Publication year: 2023

Year of publication
Publication date: 2023-09-11

Full publication date if available
Authors: Daniel Mimouni, Paul Malisani, Ji Zhu, Welington de Oliveira

List of authors in order
Landing page: https://doi.org/10.48550/arxiv.2309.05315

Publisher landing page
Open access: Yes

Whether a free full text is available
OA status: green

Open access status per OpenAlex
OA URL: https://doi.org/10.48550/arxiv.2309.05315

Direct OA link when available
Concepts: Operator (biology), Operator splitting, Applied mathematics, Mathematics, Computer science, Chemistry, Transcription factor, Repressor, Gene, Biochemistry

Top concepts (fields/topics) attached by OpenAlex
Cited by: 0

Total citation count in OpenAlex
References (count): 29

Number of works referenced by this work
Related works (count): 10

Other works algorithmically related by OpenAlex

Full payload

id	https://openalex.org/W4386651498
doi	https://doi.org/10.48550/arxiv.2309.05315
ids.doi	https://doi.org/10.48550/arxiv.2309.05315
ids.openalex	https://openalex.org/W4386651498
fwci	0.0
type	preprint
title	Computing Wasserstein Barycenter via operator splitting: the method of averaged marginals
biblio.issue
biblio.volume
biblio.last_page
biblio.first_page
topics[0].id	https://openalex.org/T11205
topics[0].field.id	https://openalex.org/fields/26
topics[0].field.display_name	Mathematics
topics[0].score	0.9835000038146973
topics[0].domain.id	https://openalex.org/domains/3
topics[0].domain.display_name	Physical Sciences
topics[0].subfield.id	https://openalex.org/subfields/2610
topics[0].subfield.display_name	Mathematical Physics
topics[0].display_name	Numerical methods in inverse problems
topics[1].id	https://openalex.org/T12056
topics[1].field.id	https://openalex.org/fields/26
topics[1].field.display_name	Mathematics
topics[1].score	0.9754999876022339
topics[1].domain.id	https://openalex.org/domains/3
topics[1].domain.display_name	Physical Sciences
topics[1].subfield.id	https://openalex.org/subfields/2613
topics[1].subfield.display_name	Statistics and Probability
topics[1].display_name	Markov Chains and Monte Carlo Methods
topics[2].id	https://openalex.org/T12100
topics[2].field.id	https://openalex.org/fields/17
topics[2].field.display_name	Computer Science
topics[2].score	0.9739000201225281
topics[2].domain.id	https://openalex.org/domains/3
topics[2].domain.display_name	Physical Sciences
topics[2].subfield.id	https://openalex.org/subfields/1703
topics[2].subfield.display_name	Computational Theory and Mathematics
topics[2].display_name	Advanced Mathematical Modeling in Engineering
is_xpac	False
apc_list
apc_paid
concepts[0].id	https://openalex.org/C17020691
concepts[0].level	5
concepts[0].score	0.6554954051971436
concepts[0].wikidata	https://www.wikidata.org/wiki/Q139677
concepts[0].display_name	Operator (biology)
concepts[1].id	https://openalex.org/C2987355758
concepts[1].level	2
concepts[1].score	0.6270747184753418
concepts[1].wikidata	https://www.wikidata.org/wiki/Q25037251
concepts[1].display_name	Operator splitting
concepts[2].id	https://openalex.org/C28826006
concepts[2].level	1
concepts[2].score	0.4878080189228058
concepts[2].wikidata	https://www.wikidata.org/wiki/Q33521
concepts[2].display_name	Applied mathematics
concepts[3].id	https://openalex.org/C33923547
concepts[3].level	0
concepts[3].score	0.44349098205566406
concepts[3].wikidata	https://www.wikidata.org/wiki/Q395
concepts[3].display_name	Mathematics
concepts[4].id	https://openalex.org/C41008148
concepts[4].level	0
concepts[4].score	0.42506885528564453
concepts[4].wikidata	https://www.wikidata.org/wiki/Q21198
concepts[4].display_name	Computer science
concepts[5].id	https://openalex.org/C185592680
concepts[5].level	0
concepts[5].score	0.0
concepts[5].wikidata	https://www.wikidata.org/wiki/Q2329
concepts[5].display_name	Chemistry
concepts[6].id	https://openalex.org/C86339819
concepts[6].level	3
concepts[6].score	0.0
concepts[6].wikidata	https://www.wikidata.org/wiki/Q407384
concepts[6].display_name	Transcription factor
concepts[7].id	https://openalex.org/C158448853
concepts[7].level	4
concepts[7].score	0.0
concepts[7].wikidata	https://www.wikidata.org/wiki/Q425218
concepts[7].display_name	Repressor
concepts[8].id	https://openalex.org/C104317684
concepts[8].level	2
concepts[8].score	0.0
concepts[8].wikidata	https://www.wikidata.org/wiki/Q7187
concepts[8].display_name	Gene
concepts[9].id	https://openalex.org/C55493867
concepts[9].level	1
concepts[9].score	0.0
concepts[9].wikidata	https://www.wikidata.org/wiki/Q7094
concepts[9].display_name	Biochemistry
keywords[0].id	https://openalex.org/keywords/operator
keywords[0].score	0.6554954051971436
keywords[0].display_name	Operator (biology)
keywords[1].id	https://openalex.org/keywords/operator-splitting
keywords[1].score	0.6270747184753418
keywords[1].display_name	Operator splitting
keywords[2].id	https://openalex.org/keywords/applied-mathematics
keywords[2].score	0.4878080189228058
keywords[2].display_name	Applied mathematics
keywords[3].id	https://openalex.org/keywords/mathematics
keywords[3].score	0.44349098205566406
keywords[3].display_name	Mathematics
keywords[4].id	https://openalex.org/keywords/computer-science
keywords[4].score	0.42506885528564453
keywords[4].display_name	Computer science
language	en
locations[0].id	doi:10.48550/arxiv.2309.05315
locations[0].is_oa	True
locations[0].source.id	https://openalex.org/S4306400194
locations[0].source.issn
locations[0].source.type	repository
locations[0].source.is_oa	True
locations[0].source.issn_l
locations[0].source.is_core	False
locations[0].source.is_in_doaj	False
locations[0].source.display_name	arXiv (Cornell University)
locations[0].source.host_organization	https://openalex.org/I205783295
locations[0].source.host_organization_name	Cornell University
locations[0].source.host_organization_lineage	https://openalex.org/I205783295
locations[0].license
locations[0].pdf_url
locations[0].version
locations[0].raw_type	article
locations[0].license_id
locations[0].is_accepted	False
locations[0].is_published
locations[0].raw_source_name
locations[0].landing_page_url	https://doi.org/10.48550/arxiv.2309.05315
indexed_in	datacite
authorships[0].author.id	https://openalex.org/A5092627738
authorships[0].author.orcid	https://orcid.org/0009-0003-8464-2253
authorships[0].author.display_name	Daniel Mimouni
authorships[0].countries	FR
authorships[0].affiliations[0].institution_ids	https://openalex.org/I70768539
authorships[0].affiliations[0].raw_affiliation_string	Mines Paris - PSL (École nationale supérieure des mines de Paris) (60, boulevard Saint-Michel 75006 Paris - France)
authorships[0].affiliations[1].institution_ids	https://openalex.org/I265217849
authorships[0].affiliations[1].raw_affiliation_string	IFPEN - IFP Energies nouvelles (1-4 avenue de Bois Préau 92500 Rueil-Malmaison - France)
authorships[0].institutions[0].id	https://openalex.org/I265217849
authorships[0].institutions[0].ror	https://ror.org/03gcbhc33
authorships[0].institutions[0].type	facility
authorships[0].institutions[0].lineage	https://openalex.org/I265217849
authorships[0].institutions[0].country_code	FR
authorships[0].institutions[0].display_name	IFP Énergies nouvelles
authorships[0].institutions[1].id	https://openalex.org/I70768539
authorships[0].institutions[1].ror	https://ror.org/04y8cs423
authorships[0].institutions[1].type	education
authorships[0].institutions[1].lineage	https://openalex.org/I190752583, https://openalex.org/I2746051580, https://openalex.org/I70768539
authorships[0].institutions[1].country_code	FR
authorships[0].institutions[1].display_name	École Nationale Supérieure des Mines de Paris
authorships[0].author_position	first
authorships[0].raw_author_name	D. Mimouni
authorships[0].is_corresponding	False
authorships[0].raw_affiliation_strings	IFPEN - IFP Energies nouvelles (1-4 avenue de Bois Préau 92500 Rueil-Malmaison - France), Mines Paris - PSL (École nationale supérieure des mines de Paris) (60, boulevard Saint-Michel 75006 Paris - France)
authorships[1].author.id	https://openalex.org/A5044073201
authorships[1].author.orcid	https://orcid.org/0000-0002-7073-155X
authorships[1].author.display_name	Paul Malisani
authorships[1].countries	FR
authorships[1].affiliations[0].institution_ids	https://openalex.org/I265217849
authorships[1].affiliations[0].raw_affiliation_string	IFPEN - IFP Energies nouvelles (1-4 avenue de Bois Préau 92500 Rueil-Malmaison - France)
authorships[1].institutions[0].id	https://openalex.org/I265217849
authorships[1].institutions[0].ror	https://ror.org/03gcbhc33
authorships[1].institutions[0].type	facility
authorships[1].institutions[0].lineage	https://openalex.org/I265217849
authorships[1].institutions[0].country_code	FR
authorships[1].institutions[0].display_name	IFP Énergies nouvelles
authorships[1].author_position	middle
authorships[1].raw_author_name	P Malisani
authorships[1].is_corresponding	False
authorships[1].raw_affiliation_strings	IFPEN - IFP Energies nouvelles (1-4 avenue de Bois Préau 92500 Rueil-Malmaison - France)
authorships[2].author.id	https://openalex.org/A5101765550
authorships[2].author.orcid	https://orcid.org/0000-0002-7812-5378
authorships[2].author.display_name	Ji Zhu
authorships[2].countries	FR
authorships[2].affiliations[0].institution_ids	https://openalex.org/I265217849
authorships[2].affiliations[0].raw_affiliation_string	IFPEN - IFP Energies nouvelles (1-4 avenue de Bois Préau 92500 Rueil-Malmaison - France)
authorships[2].institutions[0].id	https://openalex.org/I265217849
authorships[2].institutions[0].ror	https://ror.org/03gcbhc33
authorships[2].institutions[0].type	facility
authorships[2].institutions[0].lineage	https://openalex.org/I265217849
authorships[2].institutions[0].country_code	FR
authorships[2].institutions[0].display_name	IFP Énergies nouvelles
authorships[2].author_position	middle
authorships[2].raw_author_name	J. Zhu
authorships[2].is_corresponding	False
authorships[2].raw_affiliation_strings	IFPEN - IFP Energies nouvelles (1-4 avenue de Bois Préau 92500 Rueil-Malmaison - France)
authorships[3].author.id	https://openalex.org/A5110604923
authorships[3].author.orcid
authorships[3].author.display_name	Welington de Oliveira
authorships[3].countries	FR
authorships[3].affiliations[0].institution_ids	https://openalex.org/I4210107641
authorships[3].affiliations[0].raw_affiliation_string	CMA - Centre de Mathématiques Appliquées (Centre de Mathématiques Appliquées Rue Claude Daunesse CS 10207 06904 Sophia Antipolis Cedex - France)
authorships[3].institutions[0].id	https://openalex.org/I4210107641
authorships[3].institutions[0].ror	https://ror.org/012e1xn46
authorships[3].institutions[0].type	facility
authorships[3].institutions[0].lineage	https://openalex.org/I1294671590, https://openalex.org/I1294671590, https://openalex.org/I1326498283, https://openalex.org/I142476485, https://openalex.org/I4210107641, https://openalex.org/I4210141950, https://openalex.org/I4210145102
authorships[3].institutions[0].country_code	FR
authorships[3].institutions[0].display_name	Centre de Mathématiques Appliquées
authorships[3].author_position	last
authorships[3].raw_author_name	W. de Oliveira
authorships[3].is_corresponding	False
authorships[3].raw_affiliation_strings	CMA - Centre de Mathématiques Appliquées (Centre de Mathématiques Appliquées Rue Claude Daunesse CS 10207 06904 Sophia Antipolis Cedex - France)
has_content.pdf	False
has_content.grobid_xml	False
is_paratext	False
open_access.is_oa	True
open_access.oa_url	https://doi.org/10.48550/arxiv.2309.05315
open_access.oa_status	green
open_access.any_repository_has_fulltext	False
created_date	2025-10-10T00:00:00
display_name	Computing Wasserstein Barycenter via operator splitting: the method of averaged marginals
has_fulltext	False
is_retracted	False
updated_date	2025-11-06T06:51:31.235846
primary_topic.id	https://openalex.org/T11205
primary_topic.field.id	https://openalex.org/fields/26
primary_topic.field.display_name	Mathematics
primary_topic.score	0.9835000038146973
primary_topic.domain.id	https://openalex.org/domains/3
primary_topic.domain.display_name	Physical Sciences
primary_topic.subfield.id	https://openalex.org/subfields/2610
primary_topic.subfield.display_name	Mathematical Physics
primary_topic.display_name	Numerical methods in inverse problems
related_works	https://openalex.org/W2899084033, https://openalex.org/W2748952813, https://openalex.org/W4391375266, https://openalex.org/W1979597421, https://openalex.org/W2007980826, https://openalex.org/W2061531152, https://openalex.org/W3002753104, https://openalex.org/W2077600819, https://openalex.org/W412354254, https://openalex.org/W4379522615
cited_by_count	0
locations_count	1
best_oa_location.id	doi:10.48550/arxiv.2309.05315
best_oa_location.is_oa	True
best_oa_location.source.id	https://openalex.org/S4306400194
best_oa_location.source.issn
best_oa_location.source.type	repository
best_oa_location.source.is_oa	True
best_oa_location.source.issn_l
best_oa_location.source.is_core	False
best_oa_location.source.is_in_doaj	False
best_oa_location.source.display_name	arXiv (Cornell University)
best_oa_location.source.host_organization	https://openalex.org/I205783295
best_oa_location.source.host_organization_name	Cornell University
best_oa_location.source.host_organization_lineage	https://openalex.org/I205783295
best_oa_location.license
best_oa_location.pdf_url
best_oa_location.version
best_oa_location.raw_type	article
best_oa_location.license_id
best_oa_location.is_accepted	False
best_oa_location.is_published	False
best_oa_location.raw_source_name
best_oa_location.landing_page_url	https://doi.org/10.48550/arxiv.2309.05315
primary_location.id	doi:10.48550/arxiv.2309.05315
primary_location.is_oa	True
primary_location.source.id	https://openalex.org/S4306400194
primary_location.source.issn
primary_location.source.type	repository
primary_location.source.is_oa	True
primary_location.source.issn_l
primary_location.source.is_core	False
primary_location.source.is_in_doaj	False
primary_location.source.display_name	arXiv (Cornell University)
primary_location.source.host_organization	https://openalex.org/I205783295
primary_location.source.host_organization_name	Cornell University
primary_location.source.host_organization_lineage	https://openalex.org/I205783295
primary_location.license
primary_location.pdf_url
primary_location.version
primary_location.raw_type	article
primary_location.license_id
primary_location.is_accepted	False
primary_location.is_published	False
primary_location.raw_source_name
primary_location.landing_page_url	https://doi.org/10.48550/arxiv.2309.05315
publication_date	2023-09-11
publication_year	2023
referenced_works	https://openalex.org/W2058532290, https://openalex.org/W4309332481, https://openalex.org/W2970692013, https://openalex.org/W1968333723, https://openalex.org/W2312355711, https://openalex.org/W2963995333, https://openalex.org/W4232936225, https://openalex.org/W2133478409, https://openalex.org/W3034673364, https://openalex.org/W2036996178, https://openalex.org/W2953057288, https://openalex.org/W2078667299, https://openalex.org/W4302585817, https://openalex.org/W2035488027, https://openalex.org/W4206471589, https://openalex.org/W4313029060, https://openalex.org/W2963910448, https://openalex.org/W622935592, https://openalex.org/W2158131535, https://openalex.org/W3090269071, https://openalex.org/W1629559917, https://openalex.org/W2543484873, https://openalex.org/W2047894825, https://openalex.org/W2910908131, https://openalex.org/W3047066292, https://openalex.org/W2111725927, https://openalex.org/W2496350169, https://openalex.org/W205960364, https://openalex.org/W1999563417
referenced_works_count	29
abstract_inverted_index.a	31, 39, 63, 81, 115
abstract_inverted_index.In	50
abstract_inverted_index.It	14
abstract_inverted_index.WB	33, 72, 99
abstract_inverted_index.an	5
abstract_inverted_index.be	35, 92, 124
abstract_inverted_index.by	37
abstract_inverted_index.in	17
abstract_inverted_index.is	4
abstract_inverted_index.it	130
abstract_inverted_index.of	11, 108, 117
abstract_inverted_index.on	85, 140
abstract_inverted_index.to	75, 94
abstract_inverted_index.we	61, 79
abstract_inverted_index.Due	74
abstract_inverted_index.The	0
abstract_inverted_index.and	97, 126
abstract_inverted_index.are	28
abstract_inverted_index.can	34, 91, 123
abstract_inverted_index.for	8, 68, 132
abstract_inverted_index.has	104
abstract_inverted_index.the	25, 51, 69, 86, 105, 145, 148
abstract_inverted_index.(WB)	3
abstract_inverted_index.(and	119
abstract_inverted_index.When	24
abstract_inverted_index.both	95
abstract_inverted_index.data	142
abstract_inverted_index.done	36
abstract_inverted_index.etc.	23
abstract_inverted_index.even	127
abstract_inverted_index.from	144
abstract_inverted_index.have	57
abstract_inverted_index.more	52
abstract_inverted_index.sets	10, 143
abstract_inverted_index.that	90, 122
abstract_inverted_index.tool	7
abstract_inverted_index.upon	111
abstract_inverted_index.based	84
abstract_inverted_index.being	109
abstract_inverted_index.built	110
abstract_inverted_index.finds	15
abstract_inverted_index.image	21
abstract_inverted_index.their	76
abstract_inverted_index.total	59
abstract_inverted_index.where	55
abstract_inverted_index.which	103
abstract_inverted_index.whose	43
abstract_inverted_index.convex	64
abstract_inverted_index.exact)	120
abstract_inverted_index.exceed	46
abstract_inverted_index.linear	40
abstract_inverted_index.making	129
abstract_inverted_index.method	89
abstract_inverted_index.scheme	83
abstract_inverted_index.series	116
abstract_inverted_index.simple	118
abstract_inverted_index.against	137
abstract_inverted_index.applied	18, 93
abstract_inverted_index.finite,	29
abstract_inverted_index.general	53
abstract_inverted_index.masses,	60
abstract_inverted_index.methods	139
abstract_inverted_index.problem	42, 100
abstract_inverted_index.propose	62
abstract_inverted_index.setting	54
abstract_inverted_index.several	141
abstract_inverted_index.solving	38
abstract_inverted_index.balanced	96
abstract_inverted_index.colossal	77
abstract_inverted_index.measures	56
abstract_inverted_index.method's	149
abstract_inverted_index.operates	114
abstract_inverted_index.problem.	73
abstract_inverted_index.solvers'	48
abstract_inverted_index.standard	47
abstract_inverted_index.suitable	131
abstract_inverted_index.supports	27
abstract_inverted_index.Numerical	135
abstract_inverted_index.averaging	112
abstract_inverted_index.computing	30
abstract_inverted_index.datasets.	134
abstract_inverted_index.different	58
abstract_inverted_index.generally	45
abstract_inverted_index.important	6
abstract_inverted_index.introduce	80
abstract_inverted_index.measures'	26
abstract_inverted_index.measures.	13
abstract_inverted_index.nonsmooth	65
abstract_inverted_index.so-called	70
abstract_inverted_index.splitting	88
abstract_inverted_index.(balanced)	32
abstract_inverted_index.algorithm,	102
abstract_inverted_index.barycenter	2
abstract_inverted_index.dimensions	44
abstract_inverted_index.illustrate	147
abstract_inverted_index.literature	146
abstract_inverted_index.marginals,	113
abstract_inverted_index.unbalanced	71, 98
abstract_inverted_index.Wasserstein	1
abstract_inverted_index.clustering,	20
abstract_inverted_index.comparisons	136
abstract_inverted_index.dimensions,	78
abstract_inverted_index.formulation	67
abstract_inverted_index.interesting	106
abstract_inverted_index.large-scale	133
abstract_inverted_index.probability	12
abstract_inverted_index.processing,	22
abstract_inverted_index.projections	121
abstract_inverted_index.randomized,	128
abstract_inverted_index.summarizing	9
abstract_inverted_index.applications	16
abstract_inverted_index.optimization	41, 66
abstract_inverted_index.parallelized	125
abstract_inverted_index.performance.	150
abstract_inverted_index.probability,	19
abstract_inverted_index.variants.Our	101
abstract_inverted_index.capabilities.	49
abstract_inverted_index.decomposition	82
abstract_inverted_index.interpretation	107
abstract_inverted_index.Douglas-Rachford	87
abstract_inverted_index.state-of-the-art	138
cited_by_percentile_year
countries_distinct_count	1
institutions_distinct_count	4
sustainable_development_goals[0].id	https://metadata.un.org/sdg/16
sustainable_development_goals[0].score	0.5299999713897705
sustainable_development_goals[0].display_name	Peace, Justice and strong institutions
citation_normalized_percentile