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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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Bibliographic Details
Published in:arXiv.org 2023-08
Main Authors: Budzinskiy, Stanislav, Zamarashkin, Nikolai
Format: Article
Language:English
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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.
ISSN:2331-8422
DOI:10.48550/arxiv.2110.03975