Static and Dynamic Approaches to Computing Barycenters of Probability Measures on Graphs
The optimal transportation problem defines a geometry of probability measures which leads to a definition for weighted averages (barycenters) of measures, finding application in the machine learning and computer vision communities as a signal processing tool. Here, we implement a barycentric coding model for measures which are supported on a graph, a context in which the classical optimal transport geometry becomes degenerate, by leveraging a Riemannian structure on the simplex induced by a dynamic formulation of the optimal transport problem. We approximate the exponential mapping associated to the Riemannian structure, as well as its inverse, by utilizing past approaches which compute a...
| Authors | David Gentile, James M. Murphy |
|---|---|
| Primary category | stat.ML |
| Published | 27 March 2026 |
| Last updated at source | 27 March 2026 |
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