Perturbations of the Tcur Decomposition for Tensor Valued Data in the Tucker Format

The tensor CUR decomposition in the Tucker format is a special case of Tucker decomposition with a low multilinear rank, where factor matrices are obtained by selecting some columns from the mode-n unfolding of the tensor. We perform a thorough investigation of what happens to the approximations in the presence of noise. We present two forms of the tensor CUR decomposition and deduce the errors of the approximation. We illustrate how the choice of columns from each mode-n unfolding reflects the quality of the tensor CUR approximation via some numerical examples.