A multilinear Nyström algorithm for low-rank approximation of tensors in Tucker format
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914766102986752 |
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| author | Bucci, Alberto Robol, Leonardo |
| author_facet | Bucci, Alberto Robol, Leonardo |
| contents | The Nyström method offers an effective way to obtain low-rank approximation of SPD matrices, and has been recently extended and analyzed to nonsymmetric matrices (leading to the generalized Nyström method). It is a randomized, single-pass, streamable, cost-effective, and accurate alternative to the randomized SVD, and it facilitates the computation of several matrix low-rank factorizations.
In this paper, we take these advancements a step further by introducing a higher-order variant of Nyström's methodology tailored to approximating low-rank tensors in the Tucker format: the multilinear Nyström technique. We show that, by introducing appropriate small modifications in the formulation of the higher-order method, strong stability properties can be obtained. This algorithm retains the key attributes of the generalized Nyström method, positioning it as a viable substitute for the randomized higher-order SVD algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_02877 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A multilinear Nyström algorithm for low-rank approximation of tensors in Tucker format Bucci, Alberto Robol, Leonardo Numerical Analysis 15A69, 65F55 The Nyström method offers an effective way to obtain low-rank approximation of SPD matrices, and has been recently extended and analyzed to nonsymmetric matrices (leading to the generalized Nyström method). It is a randomized, single-pass, streamable, cost-effective, and accurate alternative to the randomized SVD, and it facilitates the computation of several matrix low-rank factorizations. In this paper, we take these advancements a step further by introducing a higher-order variant of Nyström's methodology tailored to approximating low-rank tensors in the Tucker format: the multilinear Nyström technique. We show that, by introducing appropriate small modifications in the formulation of the higher-order method, strong stability properties can be obtained. This algorithm retains the key attributes of the generalized Nyström method, positioning it as a viable substitute for the randomized higher-order SVD algorithm. |
| title | A multilinear Nyström algorithm for low-rank approximation of tensors in Tucker format |
| topic | Numerical Analysis 15A69, 65F55 |
| url | https://arxiv.org/abs/2309.02877 |