Multidimensional CX Decomposition of Tensors

The decomposition in terms of column space is used to reduce complexity and preserve the initial information contained in the data tensor. In this paper, we propose a multidimensional column-space decomposition to perform low rank approximation of tensors based on the CX decomposition for matrices. An algorithm is also presented to perform the approximation of the tensor based on the l2-norm. Monte Carlo simulation results are provided to illustrate the performance of the proposed CX-tensor decomposition and the associated algorithm.