Tensor train completion: Local recovery guarantees via Riemannian optimization |
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Authors: | Stanislav Budzinskiy Nikolai Zamarashkin |
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Institution: | Marchuk Institute of Numerical Mathematics RAS, Moscow, Russia |
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Abstract: | 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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Keywords: | incoherence Riemannian optimization subspace information tensor completion tensor train tensors |
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