Gradient descent on the Stiefel manifold recovers Tucker and tensor-train tensors with linear convergence whose initialization requirement and rate scale polynomially with the tensor order N.
Tensor Completion by Alternating Minimization under the Tensor Train (TT) Model
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
Using the matrix product state (MPS) representation of tensor train decompositions, in this paper we propose a tensor completion algorithm which alternates over the matrices (tensors) in the MPS representation. This development is motivated in part by the success of matrix completion algorithms which alternate over the (low-rank) factors. We comment on the computational complexity of the proposed algorithm and numerically compare it with existing methods employing low rank tensor train approximation for data completion as well as several other recently proposed methods. We show that our method is superior to existing ones for a variety of real settings.
citation-role summary
background 1
citation-polarity summary
fields
cs.LG 1years
2025 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
A Scalable Factorization Approach for High-Order Structured Tensor Recovery
Gradient descent on the Stiefel manifold recovers Tucker and tensor-train tensors with linear convergence whose initialization requirement and rate scale polynomially with the tensor order N.