Hal. Kiers et Ra. Harshman, RELATING 2 PROPOSED METHODS FOR SPEEDUP OF ALGORITHMS FOR FITTING 2-WAY AND 3-WAY PRINCIPAL COMPONENT AND RELATED MULTILINEAR MODELS, Chemometrics and intelligent laboratory systems, 36(1), 1997, pp. 31-40
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).