RELATING 2 PROPOSED METHODS FOR SPEEDUP OF ALGORITHMS FOR FITTING 2-WAY AND 3-WAY PRINCIPAL COMPONENT AND RELATED MULTILINEAR MODELS

Multilinear analysis methods such as component (and three-way componen t) analysis of very large data sets can become very computationally de manding and even infeasible unless some method is used to compress the data and/or speed up the algorithms. We discuss two previously propos ed speedup methods. (a) Alsberg and Kvalheim have proposed use of data simplification along with some new analysis algorithms. We show that their procedures solve the same problem as (b) the more general approa ch proposed (in a different context) by Carroll, Pruzansky, and Kruska l. In the latter approach, a speed improvement is attained by applying any (three-mode) PCA algorithm to a small (three-way) array derived f rom the original data. Hence, it can employ the new algorithms by Alsb erg and Kvalheim, but, as is shown in the present paper, it is easier and often more efficient to apply standard (three-mode) PCA algorithms to the small array. Finally, it is shown how the latter approach for speed improvement can also be used for other three-way models and anal ysis methods (e.g., PARAFAC/CANDECOMP and constrained three-mode PCA).