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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2511.13229 |
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| _version_ | 1866912715027513344 |
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| author | Oliver, Mary Chriselda Antony Roberts, Michael Schönlieb, Carola-Bibiane Thorpe, Matthew |
| author_facet | Oliver, Mary Chriselda Antony Roberts, Michael Schönlieb, Carola-Bibiane Thorpe, Matthew |
| contents | The manifold hypothesis posits that high-dimensional data typically resides on low-dimensional sub spaces. In this paper, we assume manifold hypothesis to investigate graph-based semi-supervised learning
methods. In particular, we examine Laplace Learning in the Wasserstein space, extending the classical
notion of graph-based semi-supervised learning algorithms from finite-dimensional Euclidean spaces to
an infinite-dimensional setting. To achieve this, we prove variational convergence of a discrete graph p- Dirichlet energy to its continuum counterpart. In addition, we characterize the Laplace-Beltrami operator
on asubmanifold of the Wasserstein space. Finally, we validate the proposed theoretical framework through
numerical experiments conducted on benchmark datasets, demonstrating the consistency of our classification performance in high-dimensional settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13229 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Laplace Learning in Wasserstein Space Oliver, Mary Chriselda Antony Roberts, Michael Schönlieb, Carola-Bibiane Thorpe, Matthew Machine Learning The manifold hypothesis posits that high-dimensional data typically resides on low-dimensional sub spaces. In this paper, we assume manifold hypothesis to investigate graph-based semi-supervised learning methods. In particular, we examine Laplace Learning in the Wasserstein space, extending the classical notion of graph-based semi-supervised learning algorithms from finite-dimensional Euclidean spaces to an infinite-dimensional setting. To achieve this, we prove variational convergence of a discrete graph p- Dirichlet energy to its continuum counterpart. In addition, we characterize the Laplace-Beltrami operator on asubmanifold of the Wasserstein space. Finally, we validate the proposed theoretical framework through numerical experiments conducted on benchmark datasets, demonstrating the consistency of our classification performance in high-dimensional settings. |
| title | Laplace Learning in Wasserstein Space |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2511.13229 |