Optimal transport with Laplacian regularization

Rémi Flamary (1, 2) , Nicolas Courty (3) , Alain Rakotomamonjy (4) , Devis Tuia (5)

1 LAGRANGE - Joseph Louis LAGRANGE
2 OCA - Observatoire de la Côte d'Azur
3 OBELIX - Environment observation with complex imagery
4 LITIS - Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes
5 LASIG - Laboratoire des Systèmes d'Information Géographique [Lausanne]

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.

Domaines: Machine Learning [stat.ML]; Traitement du signal et de l'image [eess.SP]

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⟩