|
|||||
 |
|
|
|
|
|
|
Optimal transport and
barycenters for dendritic measures
Young-Heon Kim, Brendan Pass and David J. Schneider |
|
Vol. 2 (2020), No. 3, 581–601
|
Abstract |
|
We introduce and study a variant of the Wasserstein distance on the space of probability measures, specially designed to deal with measures whose support has a dendritic, or tree-like structure with a particular direction of orientation. Our motivation is the comparison of and interpolation between plants’ root systems. We characterize barycenters with respect to this metric, and establish that the interpolations of root-like measures, using this new metric, are also root-like, in a certain sense; this property fails for conventional Wasserstein barycenters. We also establish geodesic convexity with respect to this metric for a variety of functionals, some of which we expect to have biological importance. |
Keywords
optimal transport, dendritic measures,
layerwise-Wasserstein distance, plant root architecture
|
Mathematical Subject Classification 2010
Primary: 49K99
Secondary: 92C80
|
Milestones
Received: 10 October 2019
Revised: 21 February 2020
Accepted: 28 March 2020
Published: 17 November 2020
|
Authors |
| Young-Heon Kim | |
| Department of Mathematics University of British Columbia Vancouver, BC Canada |
|
| Brendan Pass | |
| Department of Mathematical and
Statistical Sciences University of Alberta Edmonton, AB Canada |
|
| David J. Schneider | |
| Global Institute for Food
Security University of Saskatchewan Saskatoon, SK Canada |
|
