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We propose a numerical method to obtain an adequate value for the upper boundon the rank for the tensor completion problem on the variety of third-ordertensors of bounded tensor-train rank. The method is inspired by theparametrization of the tangent cone derived by Kutschan (2018). A proof of theadequacy of the upper bound for a related low-rank tensor approximation problemis given and an estimated rank is defined to extend the result to the low-ranktensor completion problem. Some experiments on synthetic data illustrate theapproach and show that the method is very robust, e.g., to noise on the data.

Rank Estimation for Third-Order Tensor Completion in the Tensor-Train Format