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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2511.07898 |
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Table des matières:
- 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.