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Authors = Remi Flamary

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33 pages, 1731 KiB  
Article
Fused Gromov-Wasserstein Distance for Structured Objects
by Titouan Vayer, Laetitia Chapel, Remi Flamary, Romain Tavenard and Nicolas Courty
Algorithms 2020, 13(9), 212; https://doi.org/10.3390/a13090212 - 31 Aug 2020
Cited by 62 | Viewed by 13220
Abstract
Optimal transport theory has recently found many applications in machine learning thanks to its capacity to meaningfully compare various machine learning objects that are viewed as distributions. The Kantorovitch formulation, leading to the Wasserstein distance, focuses on the features of the elements of [...] Read more.
Optimal transport theory has recently found many applications in machine learning thanks to its capacity to meaningfully compare various machine learning objects that are viewed as distributions. The Kantorovitch formulation, leading to the Wasserstein distance, focuses on the features of the elements of the objects, but treats them independently, whereas the Gromov–Wasserstein distance focuses on the relations between the elements, depicting the structure of the object, yet discarding its features. In this paper, we study the Fused Gromov-Wasserstein distance that extends the Wasserstein and Gromov–Wasserstein distances in order to encode simultaneously both the feature and structure information. We provide the mathematical framework for this distance in the continuous setting, prove its metric and interpolation properties, and provide a concentration result for the convergence of finite samples. We also illustrate and interpret its use in various applications, where structured objects are involved. Full article
(This article belongs to the Special Issue Efficient Graph Algorithms in Machine Learning)
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