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Conference Papers Year : 2022

Optimal Tensor Transport

Tanguy Kerdoncuff
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Rémi Emonet
Marc Sebban

Abstract

Optimal Transport (OT) has become a popular tool in machine learning to align finite datasets typically lying in the same vector space. To expand the range of possible applications, Co-Optimal Transport (Co-OT) jointly estimates two distinct transport plans, one for the rows (points) and one for the columns (features), to match two data matrices that might use different features. On the other hand, Gromov Wasserstein (GW) looks for a single transport plan from two pairwise intra-domain distance matrices. Both Co-OT and GW can be seen as specific extensions of OT to more complex data. In this paper, we propose a unified framework, called Optimal Tensor Transport (OTT), which takes the form of a generic formulation that encompasses OT, GW and CoOT and can handle tensors of any order by learning possibly multiple transport plans. We derive theoretical results for the resulting new distance and present an efficient way for computing it. We further illustrate the interest of such a formulation in Domain Adaptation and Comparison-based Clustering.
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Dates and versions

hal-03479241 , version 1 (14-12-2021)

Identifiers

  • HAL Id : hal-03479241 , version 1

Cite

Tanguy Kerdoncuff, Michaël Perrot, Rémi Emonet, Marc Sebban. Optimal Tensor Transport. AAAI, Feb 2022, Vancouver, Canada. ⟨hal-03479241⟩
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