Weighted Low-rank Approximation via Stochastic Gradient Descent on Manifolds
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866910835942621184 |
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| author | Xu, Conglong Yang, Peiqi Wu, Hao |
| author_facet | Xu, Conglong Yang, Peiqi Wu, Hao |
| contents | We solve a regularized weighted low-rank approximation problem by a stochastic gradient descent on a manifold. To guarantee the convergence of our stochastic gradient descent, we establish a convergence theorem on manifolds for retraction-based stochastic gradient descents admitting confinements. On sample data from the Netflix Prize training dataset, our algorithm outperforms the existing stochastic gradient descent on Euclidean spaces. We also compare the accelerated line search on this manifold to the existing accelerated line search on Euclidean spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_14174 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weighted Low-rank Approximation via Stochastic Gradient Descent on Manifolds Xu, Conglong Yang, Peiqi Wu, Hao Optimization and Control Artificial Intelligence Machine Learning We solve a regularized weighted low-rank approximation problem by a stochastic gradient descent on a manifold. To guarantee the convergence of our stochastic gradient descent, we establish a convergence theorem on manifolds for retraction-based stochastic gradient descents admitting confinements. On sample data from the Netflix Prize training dataset, our algorithm outperforms the existing stochastic gradient descent on Euclidean spaces. We also compare the accelerated line search on this manifold to the existing accelerated line search on Euclidean spaces. |
| title | Weighted Low-rank Approximation via Stochastic Gradient Descent on Manifolds |
| topic | Optimization and Control Artificial Intelligence Machine Learning |
| url | https://arxiv.org/abs/2502.14174 |