Rank Estimation for Third-Order Tensor Completion in the Tensor-Train Format
Optimization and Control
2024-09-10 v1
Abstract
We propose a numerical method to obtain an adequate value for the upper bound on the rank for the tensor completion problem on the variety of third-order tensors of bounded tensor-train rank. The method is inspired by the parametrization of the tangent cone derived by Kutschan (2018). A proof of the adequacy of the upper bound for a related low-rank tensor approximation problem is given and an estimated rank is defined to extend the result to the low-rank tensor completion problem. Some experiments on synthetic data illustrate the approach and show that the method is very robust, e.g., to noise on the data.
Cite
@article{arxiv.2309.15170,
title = {Rank Estimation for Third-Order Tensor Completion in the Tensor-Train Format},
author = {Charlotte Vermeylen and Guillaume Olikier and P. -A. Absil and Marc Van Barel},
journal= {arXiv preprint arXiv:2309.15170},
year = {2024}
}