On the correspondence between replicator dynamics and assignment flows
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...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2021
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| In: |
Proceedings in applied mathematics and mechanics
Year: 2021, Volume: 21, Issue: 1, Pages: 1-2 |
| ISSN: | 1617-7061 |
| DOI: | 10.1002/pamm.202100097 |
| Online Access: | Verlag, kostenfrei, Volltext: https://doi.org/10.1002/pamm.202100097 Verlag, kostenfrei, Volltext: https://onlinelibrary.wiley.com/doi/abs/10.1002/pamm.202100097 
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| Author Notes: | Bastian Boll, Jonathan Schwarz, and Christoph Schnörr |
| Summary: | 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. |
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| Item Description: | Gesehen am 27.03.2023 |
| Physical Description: | Online Resource |
| ISSN: | 1617-7061 |
| DOI: | 10.1002/pamm.202100097 |