Tensor train completion: local recovery guarantees via Riemannian optimization

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.

1 figure added; Accepted version

References in corpus (1)

• Note: low-rank tensor train completion with side information based on Riemannian optimization

Cited by in corpus (3)

• Entrywise tensor-train approximation of large tensors via random embeddings
• Quasioptimal alternating projections and their use in low-rank approximation of matrices and tensors
• Variational Bayesian inference for CP tensor completion with side information