Network consensus in the wasserstein metric space of probability measures

BISHOP, AN; DOUCET, A

Network consensus in the wasserstein metric space of probability measures

BISHOP, AN DOUCET, A

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Publisher:: Society for Industrial & Applied Mathematics (SIAM)
Publication Type:: Journal Article
Citation:: SIAM Journal on Control and Optimization, 2021, 59, (5), pp. 3261-3277
Issue Date:: 2021-01-01

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Field	Value	Language
dc.contributor.author	BISHOP, AN
dc.contributor.author	DOUCET, A
dc.date.accessioned	2022-05-17T19:59:02Z
dc.date.available	2022-05-17T19:59:02Z
dc.date.issued	2021-01-01
dc.identifier.citation	SIAM Journal on Control and Optimization, 2021, 59, (5), pp. 3261-3277
dc.identifier.issn	0363-0129
dc.identifier.issn	1095-7138
dc.identifier.uri	http://hdl.handle.net/10453/157467
dc.description.abstract	Distributed consensus in the Wasserstein metric space of probability measures on the real line is introduced in this work. Convergence of each agent's measure to a common measure is proven under a weak network connectivity condition. The common measure reached at each agent is one minimizing a weighted sum of its Wasserstein distance to all initial agent measures. This measure is known as the Wasserstein barycenter. Special cases involving Gaussian measures, empirical measures, and time-invariant network topologies are considered, where convergence rates and average-consensus results are given. This work has possible applicability in computer vision, machine learning, clustering, and estimation.
dc.language	en
dc.publisher	Society for Industrial & Applied Mathematics (SIAM)
dc.relation.ispartof	SIAM Journal on Control and Optimization
dc.relation.isbasedon	10.1137/19M1268252
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	0102 Applied Mathematics, 0906 Electrical and Electronic Engineering, 0913 Mechanical Engineering
dc.subject.classification	Industrial Engineering & Automation
dc.title	Network consensus in the wasserstein metric space of probability measures
dc.type	Journal Article
utslib.citation.volume	59
utslib.for	0102 Applied Mathematics
utslib.for	0906 Electrical and Electronic Engineering
utslib.for	0913 Mechanical Engineering
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Strength - CHT - Health Technologies
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Biomedical Engineering
pubs.organisational-group	/University of Technology Sydney/Centre for Health Technologies (CHT)
utslib.copyright.status	open_access	*
dc.date.updated	2022-05-17T19:59:00Z
pubs.issue	5
pubs.publication-status	Published
pubs.volume	59
utslib.citation.issue	5

Abstract:

Distributed consensus in the Wasserstein metric space of probability measures on the real line is introduced in this work. Convergence of each agent's measure to a common measure is proven under a weak network connectivity condition. The common measure reached at each agent is one minimizing a weighted sum of its Wasserstein distance to all initial agent measures. This measure is known as the Wasserstein barycenter. Special cases involving Gaussian measures, empirical measures, and time-invariant network topologies are considered, where convergence rates and average-consensus results are given. This work has possible applicability in computer vision, machine learning, clustering, and estimation.

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http://hdl.handle.net/10453/157467