2023/03/24 by Clément Sarrazin, Bernhard Schmitzer, Sarrazin, Clément +1
Computer Science · Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Morphological variations and asymmetry #Optimization and Control (math.OC) #Statistical Methods and Inference #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2303.13901
openalex publication_date 2023/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Optimal transport is a geometrically intuitive, robust and flexible metric for sample comparison in data analysis and machine learning. Its formal Riemannian structure allows for a local linearization via a tangent space approximation. This in turn leads to a reduction of computational complexity and simplifies combination with other methods that require a linear structure. Recently this approach has been extended to the unbalanced Hellinger--Kantorovich (HK) distance. In this article we further extend the framework in various ways, including measures on manifolds, the spherical HK distance, a study of the consistency of discretization via the barycentric projection, and the continuity properties of the logarithmic map for the HK distance.