Optimal Transport with Relaxed Marginal Constraints

Optimal transport (OT) is a principled approach for matching, having achieved success in diverse applications such as tracking and cluster alignment. It also the core computation problem solving Wasserstein metric between probabilistic distributions, which has been increasingly used machine learning. Despite its popularity, marginal constraints of OT impose fundamental limitations. For some matching or pattern extraction problems, framework not suitable, post-processing solution often unsatisfactory. In this paper, we extend by new optimization formulation called Optimal Transport with Relaxed Marginal Constraints (OT-RMC). Specifically, relax introducing penalty on deviation from constraints. Connections standard are revealed both theoretically experimentally. We demonstrate how OT-RMC can easily adapt to various tasks three highly different image analysis single-cell data analysis. Quantitative comparisons have made another commonly scheme show remarkable advantages OT-RMC.