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NEPv Approach for Optimization on Stiefel Manifold with the $(2,1)$-norm Regularization — arXiv:2609.26675

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.26675
License (as archived): CC0-1.0
Archived: 2026-10-08T15:55:32.515Z
SHA-256 of the archived text: 243ee067098ac5929b72a688839feec5e47215108da3a10e008adaea1ff2ee13
Stable URL of this page: https://metraipolis.com/documento/dc_92007ef2cc5a

How to cite

NEPv Approach for Optimization on Stiefel Manifold with the $(2,1)$-norm Regularization — arXiv:2609.26675 — arXiv (en), https://arxiv.org/abs/2609.26675 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_92007ef2cc5a (Metraipolis archive dc_92007ef2cc5a, sha256 243ee067098ac5929b72a688839feec5e47215108da3a10e008adaea1ff2ee13)

BibTeX

@misc{dc92007ef2cc5a,
  title = {NEPv Approach for Optimization on Stiefel Manifold with the $(2,1)$-norm Regularization — arXiv:2609.26675},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.26675},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_92007ef2cc5a; sha256 243ee067098ac5929b72a688839feec5e47215108da3a10e008adaea1ff2ee13},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.26675. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Row-sparse projection provides a useful tool in machine learning (ML) when it comes to, for example, feature selection, aiming to choose most relevant features for various ML objectives. One way to seek a high quality row-sparse projection is to combine an ML objective, such as the ones for PCA, LDA, and OCCA, with the matrix $(2,1)$-norm regularization which is nonsmooth. Such combinations result in challenging optimization problems on the Stiefel manifold that need to be solved efficiently. In this paper, a unifying NEPv framework is established to efficiently deal with optimization on the Stiefel manifold with the $(2,1)$-norm regularization. The effect of the $(2,1)$-norm regularization is also investigated. The wide applicability of the framework is demonstrated through the combinations of common learning objectives in today's data science applications with the $(2,1)$-norm regularization. Numerical experiments are presented to illustrate the use of the NEPv approach and to gain insights as to what a proper regularizing parameter should have in real-world applications.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-23 in math.NA).
Categorie arXiv: Numerical Analysis (math.NA).
Pagina del lavoro: https://arxiv.org/abs/2609.26675 — 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 2026-10-08T15:15:47.525Z dalla pagina https://arxiv.org/catchup/math.NA/2026-09-23?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).