A PARAFAC-ALS variant for fitting large datasets

The PARAFAC-ALS algorithm is the most widely used procedure for approximating arrays with a trilinear structure because it provides least squares solutions and delivers consistent outputs. Nonetheless, it is particularly slow at converging especially under challenging conditions, i.e. data multicollinearity, high factors’ congruence and over-factoring. This shortcoming can be quite problematic when dealing with three-way arrays of large dimensions. More efficient procedures can be employed, such as ATLD, however they are far less reliable. As an alternative, ATLD and ALS can be combined in a multi-optimization procedure in order to increase efficiency without reducing accuracy. This novel approach has been carried out and tested on artificial and real data.