Deflation method for CANDECOMP/PARAFAC tensor decomposition

CANDECOMP/PARAFAC tensor decomposition (CPD) approximates multiway data by rank-1 tensors. Unlike matrix decomposition, the procedure which estimates the best rank-R tensor approximation through R sequential best rank-1 approximations does not work for tensors, because the deflation does not always reduce the tensor rank. In this paper we propose a novel deflation method for the problem in which rank R does not exceed the tensor dimensions. A rank-R CPD can be performed through (R - 1) rank-1 reductions. At each deflation stage, the residue tensor is constrained to have a reduced multilinear rank.