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Regularized Coupling Maps on Matrix Polytopes: From Assignment to Graph Matching and Optimal Transport — arXiv:2608.29299

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.29299
License (as archived): CC0-1.0
Archived: 2026-10-17T09:02:48.612Z
SHA-256 of the archived text: de4fbac0c3262c29535cca73f6efb4bef66b3278e28d9fc793690cb93dc2421c
Stable URL of this page: https://metraipolis.com/documento/dc_7ab76bb61368

How to cite

Regularized Coupling Maps on Matrix Polytopes: From Assignment to Graph Matching and Optimal Transport — arXiv:2608.29299 — arXiv (en), https://arxiv.org/abs/2608.29299 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_7ab76bb61368 (Metraipolis archive dc_7ab76bb61368, sha256 de4fbac0c3262c29535cca73f6efb4bef66b3278e28d9fc793690cb93dc2421c)

BibTeX

@misc{dc7ab76bb61368,
  title = {Regularized Coupling Maps on Matrix Polytopes: From Assignment to Graph Matching and Optimal Transport — arXiv:2608.29299},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.29299},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_7ab76bb61368; sha256 de4fbac0c3262c29535cca73f6efb4bef66b3278e28d9fc793690cb93dc2421c},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.29299. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Three classical problems-linear assignment, graph matching, and optimal transport-share a common structure: they seek an optimal matrix-valued coupling on a matrix polytope. We study regularized coupling maps that encompass two families of regularization: entropy/KL regularization, which exponentiates the input score matrix and projects it onto the relevant matrix polytope via the KL-projection; and the Frobenius/Euclidean regularization, which performs the Euclidean projection of the scaled input matrix onto the same polytope. We trace how these two geometries yield complementary algorithmic tools for graph matching (CSGO, ASM, FRAM) and optimal transport (IP-EOT, PSN). The regularized coupling map serves as a direction generator in graph matching and as a solution representation in optimal transport, with the regularizer determining the geometry and the outer task determining the precision standard.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-01 in math.OC).
Categorie arXiv: Optimization and Control (math.OC).
Pagina del lavoro: https://arxiv.org/abs/2608.29299 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-17T08:40:19.734Z dalla pagina https://arxiv.org/catchup/math.OC/2026-09-01?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).