Recent developments in CANDECOMP/PARAFAC algorithms: a critical review

Several recently proposed algorithms for fitting the PARAFAC model are investigated and compared to more established alternatives. Alternating least squares (ALS), direct trilinear decomposition (DTLD), alternating trilinear decomposition (ATLD), self-weighted alternating trilinear decomposition (SWATLD), pseudo alternating least squares (PALS), alternating coupled vectors resolution (ACOVER), alternating slice-wise diagonalization (ASD) and alternating coupled matrices resolution (ACOMAR) are compared on both simulated and real data. For the recent algorithms, only unconstrained three-way models can be fitted. In contrast, for example, ALS allows modeling of higher-order data, as well as incorporating constraints on the parameters and handling of missing data. Nevertheless, for three-way data, the newer algorithms are interesting alternatives. It is found that the ALS estimated models are generally of a better quality than any of the alternatives even when overfactoring the model, but it is also found that ALS is significantly slower. Based on the results (in particular the poor performance of DTLD), it is advised that (a slightly modified) ASD may be a good alternative to ALS when a faster algorithm is desired.