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Optimal transport with Laplacian regularization

Abstract : We propose a method based on optimal transport for empirical distributions with Laplacian regularization (LOT). Laplacian regularization is a graph-based regu-larization that can encode neighborhood similarity between samples either on the final position of the transported samples or on their displacement. In both cases, LOT is expressed as a quadratic programming problem and can be solved with a Frank-Wolfe algorithm with optimal step size. Result on domain adaptation and a shape matching problems show the interest of using this regularization in optimal transport.
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https://hal.archives-ouvertes.fr/hal-01103076
Contributor : Nicolas Courty <>
Submitted on : Wednesday, January 14, 2015 - 9:00:14 AM
Last modification on : Friday, July 10, 2020 - 4:08:45 PM
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Rémi Flamary, Nicolas Courty, Alain Rakotomamonjy, Devis Tuia. Optimal transport with Laplacian regularization. NIPS 2014, Workshop on Optimal Transport and Machine Learning, Dec 2014, Montréal, Canada. ⟨hal-01103076⟩

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