2023 31st European Signal Processing Conference (EUSIPCO) 2023
DOI: 10.23919/eusipco58844.2023.10289827
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Rank Estimation for Third-Order Tensor Completion in the Tensor-Train Format

Charlotte Vermeylen,
Guillaume Olikier,
P.-A. Absil
et al.

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 syntheti… Show more

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