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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/2511.07898 |
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| _version_ | 1866914150385451008 |
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| author | Xiao, Chuanfu Zeng, Jiaxin |
| author_facet | Xiao, Chuanfu Zeng, Jiaxin |
| contents | Tensors, especially higher-order tensors, are typically represented in low-rank formats to preserve the main information of the high-dimensional data while saving memory space. In practice, only a small fraction elements in high-dimensional data are of interest, such as the $k$ largest or smallest elements. Thus, retrieving the $k$ largest/smallest elements from a low-rank tensor is a fundamental and important task in a wide variety of applications. In this paper, we first model the top-$k$ elements retrieval problem to a continuous constrained optimization problem. To address the equivalent optimization problem, we develop a block-alternating iterative algorithm that decomposes the original problem into a sequence of small-scale subproblems. Leveraging the separable summation structure of the objective function, a heuristic algorithm is proposed to solve these subproblems in an alternating manner. Numerical experiments with tensors from synthetic and real-world applications demonstrate that the proposed algorithm outperforms existing methods in terms of accuracy and stability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_07898 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Novel Block-Alternating Iterative Algorithm for Retrieving Top-$k$ Elements from Factorized Tensors Xiao, Chuanfu Zeng, Jiaxin Numerical Analysis Tensors, especially higher-order tensors, are typically represented in low-rank formats to preserve the main information of the high-dimensional data while saving memory space. In practice, only a small fraction elements in high-dimensional data are of interest, such as the $k$ largest or smallest elements. Thus, retrieving the $k$ largest/smallest elements from a low-rank tensor is a fundamental and important task in a wide variety of applications. In this paper, we first model the top-$k$ elements retrieval problem to a continuous constrained optimization problem. To address the equivalent optimization problem, we develop a block-alternating iterative algorithm that decomposes the original problem into a sequence of small-scale subproblems. Leveraging the separable summation structure of the objective function, a heuristic algorithm is proposed to solve these subproblems in an alternating manner. Numerical experiments with tensors from synthetic and real-world applications demonstrate that the proposed algorithm outperforms existing methods in terms of accuracy and stability. |
| title | A Novel Block-Alternating Iterative Algorithm for Retrieving Top-$k$ Elements from Factorized Tensors |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2511.07898 |