https://github.com/ocramz/assignment-riemann-opt

minimum bipartite matching via Riemann optimization
https://github.com/ocramz/assignment-riemann-opt

bipartite-matching manifold-optimization riemannian-optimization sgd

Last synced: 17 days ago
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minimum bipartite matching via Riemann optimization

• Host: GitHub
• URL: https://github.com/ocramz/assignment-riemann-opt
• Owner: ocramz
• Created: 2023-12-10T15:53:26.000Z (about 1 year ago)
• Default Branch: main
• Last Pushed: 2023-12-21T13:46:04.000Z (about 1 year ago)
• Last Synced: 2024-10-16T14:56:23.597Z (2 months ago)
• Topics: bipartite-matching, manifold-optimization, riemannian-optimization, sgd
• Language: Python
• Homepage:
• Size: 21 MB
• Stars: 2
• Watchers: 2
• Forks: 1
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
## minimum bipartite matching via Riemann optimization



A sample run, with cost lower bound (LB) given by the combinatorial (Munkres) solution and corresponding solution in dashed red line. In d=10, the Birkhoff polytope has 3628800 corners so it's likely SGD got stuck in a local minimum.

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Instead of a scipy one-liner ( [linear sum assignment](#assign) ), we take the panoramic route and formulate it as an optimization

problem over the manifold of doubly-stochastic matrices, hoping to end up in a corner of the [Birkhoff polytope](#birkhoff).

~~If it works I'll write a blog post about it~~ UPDATE: it works

### References

* https://en.wikipedia.org/wiki/Assignment_problem 

* https://en.wikipedia.org/wiki/Doubly_stochastic_matrix