Wasserstein Barycenter for Multi-Source Domain Adaptation

Montesuma, Eduardo Fernandes; Mboula, Fred Maurice Ngolè

doi:10.1109/cvpr46437.2021.01651

Cited by 26 publications

(14 citation statements)

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“…First, Multi-Source Domain Adaptation (MSDA) (e.g. [139]), deals with the case where source data comes from multiple, distributionally heterogeneous domains, namely P S1 , • • • , P S K . Second, Heterogeneous Domain Adaptation (HDA), is concerned with the case where source and target domain data live in incomparable spaces (e.g.…”

Section: Generalizations Of Domain Adaptationmentioning

confidence: 99%

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Cross-domain fault diagnosis through optimal transport for a CSTR process

et al. 2022

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Section: Generalizations Of Domain Adaptationmentioning

confidence: 99%

“…Emerging topics in this field include adaptation when one has many sources (e.g. [139], [142], [168]), and when distributions are supported in incomparable domains (e.g. [140]).…”

Section: Transfer Learningmentioning

confidence: 99%

Cross-domain fault diagnosis through optimal transport for a CSTR process

et al. 2022

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“…Wasserstein barycenters allow for a notion of average on the space of probability measures, which is well-adapted to the geometry of the data [3,4]. With recent progress on their computation [9,12,19,28,36,41] they establish themselves even further as a promising tool in many fields of data analysis, such as texture mixing [58], distributional clustering [76], histogram regression [10], domain adaptation [51] and unsupervised learning [63], among others.…”

Section: Introductionmentioning

confidence: 99%

Kantorovich–Rubinstein Distance and Barycenter for Finitely Supported Measures: Foundations and Algorithms

2022

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The purpose of this paper is to provide a systematic discussion of a generalized barycenter based on a variant of unbalanced optimal transport (UOT) that defines a distance between general non-negative, finitely supported measures by allowing for mass creation and destruction modeled by some cost parameter. They are denoted as Kantorovich–Rubinstein (KR) barycenter and distance. In particular, we detail the influence of the cost parameter to structural properties of the KR barycenter and the KR distance. For the latter we highlight a closed form solution on ultra-metric trees. The support of such KR barycenters of finitely supported measures turns out to be finite in general and its structure to be explicitly specified by the support of the input measures. Additionally, we prove the existence of sparse KR barycenters and discuss potential computational approaches. The performance of the KR barycenter is compared to the OT barycenter on a multitude of synthetic datasets. We also consider barycenters based on the recently introduced Gaussian Hellinger–Kantorovich and Wasserstein–Fisher–Rao distances.

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“…average on the space of probability measures, which is well-adapted to the geometry of the data [ Álvarez-Esteban et al, 2016, Anderes et al, 2016. With recent progress on their computation [Cuturi and Doucet, 2014, Bonneel et al, 2015, Kroshnin et al, 2019, Ge et al, 2019, Heinemann et al, 2020 they establish themselves even further as a promising tool in many fields of data analysis, such as texture mixing [Rabin et al, 2011], distributional clustering [Ye et al, 2017], histogram regression [Bonneel et al, 2016], domain adaptation [Montesuma and Mboula, 2021] and unsupervised learning [Schmitz et al, 2018], among others. However, a well known drawback of the Wasserstein distance and its barycenters in various applications is their limitation to measures with equal total mass.…”

Section: Introductionmentioning

confidence: 99%

Kantorovich-Rubinstein distance and barycenter for finitely supported measures: Foundations and Algorithms

Heinemann¹,

Klatt²,

Munk³

2021

Preprint

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The purpose of this paper is to provide a systematic discussion of a generalized barycenter based on a variant of unbalanced optimal transport (UOT) that defines a distance between general non-negative measures by allowing for mass creation and destruction modeled by some cost parameter. We refer to them as Kantorovich-Rubinstein (KR) barycenter and distance. We restrict our analysis to finite ground spaces as demanded for any KR based real world data analysis. In particular, we detail the influence of the cost parameter to structural properties of the KR barycenter and the KR distance. For the latter we highlight a closed form solution on ultrametric trees. The support of KR barycenters of finitely supported measures turns out to be finite and its geometry to be explicitly specified by the support of the input data measures. Additionally, we prove the existence of sparse KR barycenters and discuss potential computational approaches. The performance of the KR barycenter is compared to the OT barycenter on a multitude of synthetic data sets. We also consider barycenters based on the recently introduced Gaussian Hellinger-Kantorovich and Wasserstein-Fisher-Rao distances.

show abstract

Wasserstein Barycenter for Multi-Source Domain Adaptation

Cited by 26 publications

References 10 publications

Cross-domain fault diagnosis through optimal transport for a CSTR process

Cross-domain fault diagnosis through optimal transport for a CSTR process

Kantorovich–Rubinstein Distance and Barycenter for Finitely Supported Measures: Foundations and Algorithms

Kantorovich-Rubinstein distance and barycenter for finitely supported measures: Foundations and Algorithms

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