Error Analysis of low-rank three-way tensor factorization approach to blind source separation

In tensor factorization approach to blind separation of multidimensional sources two formulas for calculating the source tensor have emerged. In practice, it is observed that these two schemes exhibit different levels of robustness against perturbations of the factors involved in the tensor model. Motivated by both practical reasons and the will to better figure this out, we present error analyses in source tensor estimation performed by low-rank factorization of three-way tensors. To that aim, computer simulations as well as the analytical calculation of the theoretical error are carried out. The conclusions drawn from these numerical and analytical error analyses are supported by the results obtained thanks to the tensor factorization based blind decomposition of an experimental multispectral image of a skin tumor.