Rank Estimation for Third-Order Tensor Completion in the Tensor-Train Format
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910593832714240 |
|---|---|
| author | Vermeylen, Charlotte Olikier, Guillaume Absil, P. -A. Van Barel, Marc |
| author_facet | Vermeylen, Charlotte Olikier, Guillaume Absil, P. -A. Van Barel, Marc |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_15170 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rank Estimation for Third-Order Tensor Completion in the Tensor-Train Format Vermeylen, Charlotte Olikier, Guillaume Absil, P. -A. Van Barel, Marc Optimization and Control 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. |
| title | Rank Estimation for Third-Order Tensor Completion in the Tensor-Train Format |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2309.15170 |