Metraipolis › archive › dc_677fa2dc431d

A Finslerian Approach for Embedding Directed Data — arXiv:2609.37649

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.37649
License (as archived): CC0-1.0
Archived: 2026-10-07T17:33:02.679Z
SHA-256 of the archived text: 3ae616431ca9747076d5334f64890ae0435de71eab4acb61512b66988b8a9876
Stable URL of this page: https://metraipolis.com/documento/dc_677fa2dc431d

How to cite

A Finslerian Approach for Embedding Directed Data — arXiv:2609.37649 — arXiv (en), https://arxiv.org/abs/2609.37649 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_677fa2dc431d (Metraipolis archive dc_677fa2dc431d, sha256 3ae616431ca9747076d5334f64890ae0435de71eab4acb61512b66988b8a9876)

BibTeX

@misc{dc677fa2dc431d,
  title = {A Finslerian Approach for Embedding Directed Data — arXiv:2609.37649},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.37649},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_677fa2dc431d; sha256 3ae616431ca9747076d5334f64890ae0435de71eab4acb61512b66988b8a9876},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.37649. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Many datasets carry an intrinsic directionality: citations point backward in time, cells differentiate along lineages, and traffic follows preferred routes. Spectral embedding methods, including most of their extensions to directed graphs, discard this information: they symmetrize the data and map it into a Euclidean space where asymmetry cannot be represented. We instead model directed data as sampled from a Finsler manifold, whose distance depends on the direction of travel, and study the kernel operator built from this asymmetric distance. Through a moment expansion of this operator, we show that its symmetric and antisymmetric parts separate geometry from direction. As the bandwidth of the kernel vanishes, the symmetric part converges to a weighted Laplacian, recovering diffusion maps in the Riemannian case, while the antisymmetric part converges to a first-order transport operator that encodes the directionality. We prove that the corresponding graph operators, built from finitely many samples, converge uniformly and almost surely to these limits. For Randers metrics, this vector field is explicit and yields an embedding algorithm recovering both the manifold structure, from the spectrum of the symmetric part, and the underlying drift. We illustrate the approach on synthetic directed graphs and point-clouds.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-09-30 in cs.LG).
Categorie arXiv: Machine Learning (stat.ML) ; Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2609.37649 — 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 2026-10-07T16:59:48.567Z dalla pagina https://arxiv.org/catchup/cs.LG/2026-09-30?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).