An approximation method of CP rank for third-order tensor completion

We study the problem of third-order tensor completion based on low CP rank recovery. Due to the NP-hardness of the calculation of CP rank, we propose an approximation method by using the sum of ranks of a few matrices as an upper bound of CP rank. We show that such upper bound is between CP rank and the square of CP rank of a tensor. This approximation would be useful when the CP rank is very small. Numerical algorithms are developed and examples are presented to demonstrate that the tensor completion performance by the proposed method is better than that of existing methods.