Rank Estimation for Third-Order Tensor Completion in the Tensor-Train Format
(2023) Proceedings of the 31st European Signal Processing Conference (EUSIPCO 2023 — p. 965-969 (2023)
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- 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.
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Citations
Vermeylen, C., Olikier, G., Absil, P.-A., & Van Barel, M. (2023). Rank Estimation for Third-Order Tensor Completion in the Tensor-Train Format. Proceedings of the 31st European Signal Processing Conference (EUSIPCO 2023, 965-969. https://doi.org/10.48550/arXiv.2309.15170 (Original work published 2023)