On the Correspondence Between Replicator Dynamics and Assignment Flows

Bastian Boll, Jonathan Schwarz, Christoph Schnörr

Abstract: 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.