On the correspondence between replicator dynamics and assignment flows - Boll, Bastian; Schwarz, Jonathan; Schnörr, Christoph (Proceedings in applied mathematics and mechanics, 2021)
Assignment flows are smooth dynamical systems for data labeling on graphs. Although they exhibit structural similarities with the well-studied class of replicator dynamics, it is nontrivial to apply existing tools to their analysis. We propose an embedding of the underlying assignment manifold into the interior of a single probability simplex. Under this embedding, a large class of assignment flows are pushed to much higher-dimensional replicator dynamics. We demonstrate the applicability of this result by transferring a spectral decomposition of replicator dynamics to assignment flows.
Gesehen am 27.03.2023