CP model estimation with incorrect rank of factorization on large data sets

The accuracy of the ALS procedure for fitting the CP decomposition is affected by incorrect model selection due to the properties of its objective function. A study on ALS performance is presented in order to show that for large data sets this occasional shortcoming becomes prevalent. This deficiency should warn off researchers from employing ALS unless the rank of the underlying trilinear structure can be established in advance. Multi-optimization provides a possible solution: ALS can be initialized with procedures insensitive to over-factoring such as SWATLD and ATLD. In this manner it is possible to overcome factorization issues and provide a gain in efficiency without relying on computationally expensive model selection procedures.