A Review on Modern Computational Optimal Transport Methods with Applications in Biomedical Research
It provides a synthesis of existing methods for researchers in data science and biomedicine, but is incremental as it reviews rather than introduces new techniques.
This review paper surveys modern computational methods for optimal transport, focusing on regularization-based and projection-based approaches, and discusses their applications in biomedical research.
Optimal transport has been one of the most exciting subjects in mathematics, starting from the 18th century. As a powerful tool to transport between two probability measures, optimal transport methods have been reinvigorated nowadays in a remarkable proliferation of modern data science applications. To meet the big data challenges, various computational tools have been developed in the recent decade to accelerate the computation for optimal transport methods. In this review, we present some cutting-edge computational optimal transport methods with a focus on the regularization-based methods and the projection-based methods. We discuss their real-world applications in biomedical research.