Geometry of Graph Partitions via Optimal Transport
Author(s)
Abrishami, Tara; Guillen, Nestor; Rule, Parker; Schutzman, Zachary; Solomon, Justin; Weighill, Thomas; Wu, Si; ... Show more Show less
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© 2020 Tara Abrishami, Nestor Guillen, Parker Rule, We define a distance metric between partitions of a graph using machinery from optimal transport. Our metric is built from a linear assignment problem that matches partition components, with assignment cost proportional to transport distance over graph edges. We show that our distance can be computed using a single linear program without precomputing pairwise assignment costs and derive several theoretical properties of the metric. Finally, we provide experiments demonstrating these properties empirically, specifically focusing on the metric's value for new problems in ensemble-based analysis of political districting plans.
Date issued
2020Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence LaboratoryJournal
SIAM Journal on Scientific Computing
Publisher
Society for Industrial & Applied Mathematics (SIAM)