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fdWasserstein: Optimal Transport Methods for Covariance Operators of Functional Data — arXiv:2608.22921

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.22921
License (as archived): CC0-1.0
Archived: 2026-10-18T08:19:03.342Z
SHA-256 of the archived text: ca24f4ddfbbd1b1eab4667563855acb113abb7fd09a88abaa5a74dd443d9ff73
Stable URL of this page: https://metraipolis.com/documento/dc_261ae24bb995

How to cite

fdWasserstein: Optimal Transport Methods for Covariance Operators of Functional Data — arXiv:2608.22921 — arXiv (en), https://arxiv.org/abs/2608.22921 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_261ae24bb995 (Metraipolis archive dc_261ae24bb995, sha256 ca24f4ddfbbd1b1eab4667563855acb113abb7fd09a88abaa5a74dd443d9ff73)

BibTeX

@misc{dc261ae24bb995,
  title = {fdWasserstein: Optimal Transport Methods for Covariance Operators of Functional Data — arXiv:2608.22921},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.22921},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_261ae24bb995; sha256 ca24f4ddfbbd1b1eab4667563855acb113abb7fd09a88abaa5a74dd443d9ff73},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.22921. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Data increasingly arrive as collections of curves - a voice recording, a growth trajectory, a day of sensor readings - where each observation is a whole function rather than a single number. The usual question asked of such data is how the average curve differs from one group to the next. But the average is only half the picture: two populations of curves can share almost the same mean and still differ profoundly in how they fluctuate around it, and it is often this variability - the pattern of covariation within a curve - that carries the scientific signal. Comparing populations at this level means comparing their covariance operators, and statistics on covariances is impaired by their non-linearity. The fdWasserstein package equips R users with functions to make such comparisons. It is centered on the geometry of optimal transport, under which covariance operators can be meaningfully averaged, contrasted, and interpolated. It provides the Procrustes-Wasserstein distance between covariance operators, their Frechet mean (barycenter), an ANOVA-type permutation test for the equality of several covariances, principal component analysis of covariance variation, and an entropy-regularized soft clustering of curves by their covariance structure. We outline the underlying ideas, discuss the implementation and demonstrate the complete workflow on the phoneme data shipped with the package.

Tema degli esploratori: statistica e scienza dei dati (retro-catalogo arXiv: annunci del 2026-08-25 in stat.CO).
Categorie arXiv: Computation (stat.CO).
Pagina del lavoro: https://arxiv.org/abs/2608.22921 — 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 2026-10-18T08:17:34.674Z dalla pagina https://arxiv.org/catchup/stat.CO/2026-08-25?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).