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Geometric Feature Learning for Functional Data Valued on the Symmetric Positive Definite Manifold — arXiv:2609.30487

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.30487
License (as archived): CC0-1.0
Archived: 2026-10-08T02:10:26.291Z
SHA-256 of the archived text: 5dd23cb0b2915dc39421d2e90780ff7b500bba5a0eabd7d319deb7990fce3897
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How to cite

Geometric Feature Learning for Functional Data Valued on the Symmetric Positive Definite Manifold — arXiv:2609.30487 — arXiv (en), https://arxiv.org/abs/2609.30487 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ca2f424b3a06 (Metraipolis archive dc_ca2f424b3a06, sha256 5dd23cb0b2915dc39421d2e90780ff7b500bba5a0eabd7d319deb7990fce3897)

BibTeX

@misc{dcca2f424b3a06,
  title = {Geometric Feature Learning for Functional Data Valued on the Symmetric Positive Definite Manifold — arXiv:2609.30487},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.30487},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ca2f424b3a06; sha256 5dd23cb0b2915dc39421d2e90780ff7b500bba5a0eabd7d319deb7990fce3897},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.30487. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We here develop a functional neural network, termed MatFAE, for learning trajectories on the Riemannian manifold of symmetric positive definite (SPD) matrices. MatFAE features intrinsic layers that map manifold-valued functions to Euclidean vector-valued functions, followed by a functional layer that projects them into a finite-dimensional Euclidean space. Unlike most neural networks for discrete-time sequences, MatFAE treats each sequence as a continuous function and can therefore encode trajectory dynamics (e.g., first-order derivatives) in its latent representations. Additionally, the morphology of the functional weights in the functional layer offers interpretability by revealing the regions of the input functional data that contribute most to the latent representations. We justify the design principles and properties of each intrinsic layer and detail how matrix factorization is handled during backpropagation. We apply MatFAE to a range of fMRI datasets, demonstrating its ability to efficiently learn informative representations from high-dimensional SPD trajectories and its practical value for real-world neuroimaging analysis.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-09-28 in cs.LG).
Categorie arXiv: Machine Learning (cs.LG) ; Machine Learning (stat.ML).
Pagina del lavoro: https://arxiv.org/abs/2609.30487 — 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 2026-10-08T01:43:06.670Z dalla pagina https://arxiv.org/catchup/cs.LG/2026-09-28?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).