Towards a rehabilitation of the generalized rank annihilation method (GRAM)

The trilinear PARAFAC model occupies a central place in multiway analysis, because the components of a data array can often be uniquely resolved. This paper compares the resolution for a large variety of methods, namely the generalized rank annihilation method (GRAM), alternating least squares (ALS), alternating trilinear decomposition (ATLD), alternating coupled vectors resolution (ACOVER), alternating slice-wise diagonalization (ASD), alternating coupled matrices resolution (ACOMAR), self-weighted alternating trilinear decomposition (SWATLD), and pseudo alternating least squares (PALS). The comparison was conducted using Monte Carlo simulations. It was shown that GRAM performs well for moderately and highly overlapped data. These results argue strongly against the previously claimed superiority of the alternatives listed above.