scholarly journals Sharp boundary ε-regularity of optimal transport maps

2021 ◽  
Vol 381 ◽  
pp. 107603
Author(s):  
Tatsuya Miura ◽  
Felix Otto
Keyword(s):  
Optimal Transport ◽  
Sharp Boundary ◽  
Transport Maps

scholarly journals Regularity of optimal transport maps on multiple products of spheres

2013 ◽  
Vol 15 (4) ◽  
pp. 1131-1166 ◽  
Author(s):  
Alessio Figalli ◽  
Young-Heon Kim ◽  
Robert McCann
Keyword(s):  
Optimal Transport ◽  
Multiple Products ◽  
Transport Maps ◽  
Products Of Spheres

scholarly journals Parseval’s identity and optimal transport maps

2021 ◽  
Vol 170 ◽  
pp. 108989
Author(s):  
N. Ghaffari ◽  
S.G. Walker
Keyword(s):  
Optimal Transport ◽  
Transport Maps

Optimal transport maps on infinite dimensional spaces

2015 ◽  
Vol 10 (4) ◽  
pp. 715-732
Author(s):  
Shizan Fang ◽  
Vincent Nolot
Keyword(s):  
Optimal Transport ◽  
Infinite Dimensional ◽  
Transport Maps

Existence of optimal transport maps for crystalline norms

2004 ◽  
Vol 125 (2) ◽  
pp. 207-241 ◽  
Author(s):  
L. Ambrosio ◽  
B. Kirchheim ◽  
A. Pratelli
Keyword(s):  
Optimal Transport ◽  
Transport Maps

scholarly journals Partial W 2,p regularity for optimal transport maps

2017 ◽  
Vol 272 (11) ◽  
pp. 4588-4605 ◽  
Author(s):  
Shibing Chen ◽  
Alessio Figalli
Keyword(s):  
Optimal Transport ◽  
Transport Maps

scholarly journals Clustering, factor discovery and optimal transport

2020 ◽  
Author(s):  
Hongkang Yang ◽  
Esteban G Tabak
Keyword(s):  
Latent Variables ◽  
Optimal Transport ◽  
Clustering Algorithms ◽  
Data Sets ◽  
Affine Transformations ◽  
Real World Data ◽  
Continuous Version ◽  
Clustering Problem ◽  
Latent Space ◽  
Transport Maps

Abstract The clustering problem, and more generally latent factor discovery or latent space inference, is formulated in terms of the Wasserstein barycenter problem from optimal transport. The objective proposed is the maximization of the variability attributable to class, further characterized as the minimization of the variance of the Wasserstein barycenter. Existing theory, which constrains the transport maps to rigid translations, is extended to affine transformations. The resulting non-parametric clustering algorithms include $k$-means as a special case and exhibit more robust performance. A continuous version of these algorithms discovers continuous latent variables and generalizes principal curves. The strength of these algorithms is demonstrated by tests on both artificial and real-world data sets.

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