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Tensor train completion: local recovery guarantees via Riemannian optimization
In this work, we estimate the number of randomly selected elements of a tensor that with high probability guarantees local convergence of Riemannian gradient descent for tensor train completion. We derive a new bound for the orthogonal projections onto the tangent spaces based on the harmonic mean o...
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Published in: | arXiv.org 2023-08 |
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Main Authors: | , |
Format: | Article |
Language: | English |
Subjects: | |
Online Access: | Get full text |
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Summary: | In this work, we estimate the number of randomly selected elements of a tensor that with high probability guarantees local convergence of Riemannian gradient descent for tensor train completion. We derive a new bound for the orthogonal projections onto the tangent spaces based on the harmonic mean of the unfoldings' singular values and introduce a notion of core coherence for tensor trains. We also extend the results to tensor train completion with auxiliary subspace information and obtain the corresponding local convergence guarantees. |
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ISSN: | 2331-8422 |
DOI: | 10.48550/arxiv.2110.03975 |