, R n withX , a tensor with n-ranks Q n ≤ R n for all modes n. Unlike the case of SVD, there is no analytical procedure to find the best lower-rank approximation to a tensor, and Tucker decomposition algorithms search for the reduced rank tensor with the best fit (as measured by least square error) iteratively.
we use the memory-efficient MET(1) algorithm of Kolda and Sun (2008) as implemented in the Matlab Tensor Toolbox.