Distributional barycenter problem through data-driven flows
作者：
Highlights：
• A new algorithm for the solution of the optimal transport barycenter problem on manifolds is proposed.
• The algorithm allows the adoption of very general, non necessarily pairwise, cost functions.
• The algorithm overcomes the adversarial nature of the barycenter problem.
• A new cost function penalizing non-isotropic maps is introduced.
• The efficacy of the method is illustrated on synthetic examples and on the MNIST data set.
摘要
•A new algorithm for the solution of the optimal transport barycenter problem on manifolds is proposed.•The algorithm allows the adoption of very general, non necessarily pairwise, cost functions.•The algorithm overcomes the adversarial nature of the barycenter problem.•A new cost function penalizing non-isotropic maps is introduced.•The efficacy of the method is illustrated on synthetic examples and on the MNIST data set.
论文关键词：Optimal transport,Barycenter problem,Pattern visualization,Simulation,Generative models
论文评审过程：Received 16 January 2021, Revised 6 April 2022, Accepted 14 May 2022, Available online 16 May 2022, Version of Record 20 May 2022.
论文官网地址：https://doi.org/10.1016/j.patcog.2022.108795
