Unnormalized Optimal Transport
arXiv:1902.03367 · doi:10.1016/j.jcp.2019.108940
Abstract
We propose an extension of the computational fluid mechanics approach to the Monge-Kantorovich mass transfer problem, which was developed by Benamou-Brenier. Our extension allows optimal transfer of unnormalized and unequal masses. We obtain a one-parameter family of simple modifications of the formulation in [4]. This leads us to a new Monge-Ampere type equation and a new Kantorovich duality formula. These can be solved efficiently by, for example, the Chambolle-Pock primal-dual algorithm. This solution to the extended mass transfer problem gives us a simple metric for computing the distance between two unnormalized densities. The L1 version of this metric was shown in [23] (which is a precursor of our work here) to have desirable properties.
References in corpus (6)
- Wasserstein GAN
- Learning with a Wasserstein Loss
- Generalized Wasserstein distance and its application to transport equations with source
- Optimal Entropy-Transport problems and a new Hellinger-Kantorovich distance between positive measures
- A new optimal transport distance on the space of finite Radon measures
- Seismic Inversion and the Data Normalization for Optimal Transport
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